The rms current flowing through an RLC series circuit increases as the capacitive reactance is decreased. - False
The rms (root mean square) current flowing through an RLC series circuit does not increase as the capacitive reactance is decreased. In fact, as the capacitive reactance (XC) decreases, the impedance of the circuit decreases, which results in an increase in the current magnitude.
In an RLC series circuit, the impedance (Z) is given by the formula:
Z = √(R^2 + (XL - XC)^2)
Where R is the resistance, XL is the inductive reactance, and XC is the capacitive reactance.
As XC decreases, the term (XL - XC) in the above formula becomes larger, resulting in a larger overall impedance. According to Ohm's Law (V = I * Z), for a given voltage (V), a larger impedance leads to a smaller current (I).
Therefore, as the capacitive reactance is decreased in an RLC series circuit, the rms current actually increases.
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Two converging lenses are separated by a distance L = 65 [cm]. The focal length of each lens is equal to fp = f2 = 15 (cm). An object is placed at distance so = 30 (cm) to the left of Lens-1.
Calculate the image distance s'y formed by Lens-1.
If the image distance formed by Lens- 1 is s'; = 32, calculate the transverse magnification M of Lens-1. If the image distance formed by Lens- 1 is s'ı = 32, find the distance s2 between Lens-2 and the image formed by Lens-1. If the image distance formed by Lens- 1 is s'ı = 32, find the distance s2 between Lens-2 and the image formed by Lens-1.
If the distance between Lens-2 and the image formed by Lens-l is s2 = 13 [cm], calculate the final image distance s'2.
Focal length (fp = 15 cm) and distance between Lens-2 and the image formed by Lens-1 (s2 = 13 cm) into the lens formula, we can determine the final image distance s'2.
The image distance s'y formed by Lens-1 can be calculated using the lens formula and the given parameters. By substituting the values of focal length (fp = 15 cm) and object distance (so = 30 cm) into the lens formula, we can solve for s'y. The transverse magnification M of Lens-1 can be calculated by dividing the image distance formed by Lens-1 (s'y) by the object distance (so). Given that s'y = 32 cm, we can substitute these values into the formula to find the transverse magnification M. To find the distance s2 between Lens-2 and the image formed by Lens-1, we can use the lens formula once again. By substituting the given values of focal length (fp = 15 cm) and image distance formed by Lens-1 (s'y = 32 cm) into the lens formula, we can calculate s2. Lastly, to calculate the final image distance s'2, we need to use the lens formula one more time. By substituting the values of focal length (fp = 15 cm) and distance between Lens-2 and the image formed by Lens-1 (s2 = 13 cm) into the lens formula, we can determine the final image distance s'2.
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A motorcyclist is making an electric vest that, when connected to the motorcycle's 12 V battery, will alarm her on cold rides. She is using a .21 -mm- diameter copper wire, and she wants a current of 4.6 A in the wire. What length wire must she use?
The motorcyclist must use a copper wire of approximately 165 meters to achieve a current of 4.6 A when connected to a 12 V battery.
To determine the length of the wire required, we need to consider the relationship between current, voltage, and resistance. Ohm's Law states that the recent passing through a conductor is directly proportional to the voltage across it and inversely proportional to its resistance. In this case, the voltage is fixed at 12 V battery, and the desired current is 4.6 A.
The resistance of a wire can be calculated using the formula R = (ρ * L) / A, where R is the resistance, ρ is the resistivity of the material (copper in this case), L is the length of the wire, and A is the cross-sectional area of the wire.
Since we know the diameter of the wire (21 mm), we can calculate its radius (10.5 mm or 0.0105 m) and use it to find the cross-sectional area (A = π * r^2). By substituting the values into the formula, we can solve for the length of the wire.
Assuming the resistivity of copper is approximately 1.68 × 10^-8 ohm-m, the calculation becomes:
R = (1.68 × 10^-8 ohm-m * L) / (π * (0.0105 m)^2)
By rearranging the formula and solving for L, we find that the length of the wire should be approximately 165 meters to achieve a current of 4.6 A.
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The ideal gas in a container is under a pressure of 17.0 atm at a temperature of 25.0°C. If half of the gas is released from the container and the temperature is increased by 42.0°C, what is the final pressure of the gas?
The final pressure of the gas is 22.5 atm.
To solve this problem, we can use the combined gas law, which relates the initial and final states of a gas sample.
The combined gas law is given by:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where P1 and P2 are the initial and final pressures, V1 and V2 are the initial and final volumes (assuming the volume remains constant in this case), and T1 and T2 are the initial and final temperatures.
Given:
P1 = 17.0 atm (initial pressure)
T1 = 25.0°C (initial temperature)
ΔT = 42.0°C (change in temperature)
P2 = ? (final pressure)
First, let's convert the temperatures to Kelvin:
T1 = 25.0°C + 273.15 = 298.15 K
ΔT = 42.0°C = 42.0 K
Next, we can rearrange the combined gas law equation to solve for P2:
P2 = (P1 * V1 * T2) / (V2 * T1)
Since the volume remains constant, V1 = V2, and we can simplify the equation to:
P2 = (P1 * T2) / T1
Substituting the given values, we have:
P2 = (17.0 atm * (298.15 K + 42.0 K)) / 298.15 K = 22.5 atm
Therefore, the final pressure of the gas is 22.5 atm.
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QUESTIONS Use the ammeter and voltmeter reading to find the percentage error in power where P-VI OO 10 2001 MA io O 0.01 0.001 2 0.02
Using the ammeter and voltmeter reading the percentage error in power is 0.175%.
Given:
Potential Difference (V) = 10V,
Current (I) = 2A,
Resistance (R) = V/I
= 10/2
= 5 Ω
Error in Voltage (ΔV) = ± 0.01V
Errors in Current (ΔI) = ± 0.001A
Error in Power (ΔP) = ?
Percentage Error in Power = (ΔP/P) × 100%
Power, P = V × I
= 10 × 2
= 20 W
Let's find the maximum and minimum values of power with their respective errors.
Minimum Value of Power, Pmin = (V - ΔV) × (I - ΔI)
= (10 - 0.01) × (2 - 0.001)
= 19.96 W
Maximum Value of Power, Pmax = (V + ΔV) × (I + ΔI)
= (10 + 0.01) × (2 + 0.001)
= 20.03 W
The mean value of power is:
Pmean = (Pmax + Pmin)/2
= (20.03 + 19.96)/2
= 19.995 W
ΔP = Pmax - Pmean
= 20.03 - 19.995
= 0.035 W
Percentage Error in Power = (ΔP/P) × 100%
= (0.035/19.995) × 100%
= 0.175%
∴ The percentage error in power is 0.175%.
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What is the separation between two slits for which 620-nm orange light has its first maximum at an angle of 34 deg? Hint The separation between two slits is um (microns).
The separation between the two slits is approximately 1.16 microns.
To find the separation between two slits, we can use the formula for the angle of the first maximum in the double-slit interference pattern:
sin(θ) = m * λ / d
Where:
θ = angle of the first maximum
m = order of the maximum (in this case, m = 1 for the first maximum)
λ = wavelength of the light
d = separation between the slits
Rearranging the formula to solve for d, we have:
d = m * λ / sin(θ)
Given:
θ = 34 degrees
λ = 620 nm = 620 x 10^(-9) m
m = 1
Substituting the values into the formula:
d = (1 * 620 x 10^(-9) m) / sin(34 degrees)
Calculating the value:
d ≈ 1.16 x 10^(-6) m
Converting to microns:
d ≈ 1.16 μm
Therefore, the separation between the two slits is approximately 1.16 microns.
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1. () The magnetic flux through a coil containing 10 loops changes from 20Wb to-20Wb in 0.03s. Find the induced voltage e. 2. () A loop with radius r = 20cm is initially oriented perpendicular to 1.27 magnetic field. If the loop is rotated 90° in 0.4s. Find the induced voltage e in the loop. 3. pt) If the electric field of an EM wave has a peak magnitude of 0.05V/m. Find the peak magnitude of the magnetic field. 4. () The magnetic field of a plane EM wave is given by B = Bo cos(kz-wt)j- Indicate: a) The direction of propagation of the wave b) The direction of E. 5. () How long it takes for the light of a star to reach us if the star is at a distance of 8 x 10¹0km from Earth. 6. () Find the wavelength of a 10 Hz EM wave.
The induced voltage in the coil is 1333.33 V. The change in magnetic flux and the induced voltage is 0.The direction of propagation and E is the z-direction and -y-direction. The wavelength is 30 million meters.
To find the induced voltage (e) in the coil, we can use Faraday's law of electromagnetic induction, which states that the induced voltage is equal to the rate of change of magnetic flux through the coil. Mathematically, it is given by: e = -N * ΔΦ/Δt where N is the number of loops in the coil, ΔΦ is the change in magnetic flux, and Δt is the change in time.
N = 10 loops
ΔΦ = -20 Wb - 20 Wb = -40 Wb (change in magnetic flux)
Δt = 0.03 s (change in time)
Substituting the values into the equation, we get:
e = -10 (-40 Wb) / 0.03 s
e = 1333.33 V
Therefore, the induced voltage in the coil is 1333.33 V.
2. To find the induced voltage (e) in the rotated loop, we can use Faraday's law again. The induced voltage is given by the rate of change of magnetic flux through the loop, which is related to the change in the area enclosed by the loop.
r = 20 cm = 0.2 m (radius of the loop)
B = 1.27 T (magnetic field strength)
θ = 90° (angle of rotation)
Δt = 0.4 s (change in time)
The change in area (ΔA) is given by:
ΔA = π(r² - 0) = π (0.2²) = 0.04π m²
The change in magnetic flux (ΔΦ) is:
ΔΦ = B ΔA cos(θ) = 1.27 T (0.04π m²)cos(90°) = 0
Since the change in magnetic flux is 0, the induced voltage (e) in the loop is also 0.
3. The relationship between the electric field (E) and the magnetic field (B) in an electromagnetic wave is given by:
E = cB where c is the speed of light in a vacuum, approximately equal to 3 x 10⁸ m/s.
Given:
[tex]E_{peak} = 0.05 V/m[/tex] (peak magnitude of the electric field)
So, [tex]B_{peak} = \frac {E_{peak}}{c} = \frac {(0.05 V/m)}{(3 \times 10^8 m/s)} = 1.67 \times 10^{-10} T[/tex]
Therefore, the peak magnitude of the magnetic field is 1.67 x 10^-10 T.
4. a) The direction of propagation of the electromagnetic wave can be determined by the direction of the wavevector (k). In the given equation, the wavevector (k) points in the z-direction (kz), which indicates that the wave propagates in the positive or negative z-direction.
b) The direction of the electric field (E) can be determined by the coefficient multiplying the j-component in the given equation. In this case, the j-component is negative (-cos(kz - wt)), which means the electric field is in the negative y-direction.
5. To find the time it takes for light from a star to reach us, we can use the speed of light as a reference.
Distance to the star [tex]= 8 \times 10^{10} km = 8 \times 10^{13} m[/tex]
The time taken for light to travel from the star to Earth can be calculated using the formula:
Time = Distance / Speed
Using the speed of light (c = 3 x 10⁸ m/s), we have:
Time = (8 x 10¹³ m) / (3 x 10⁸ m/s)
Time ≈ 2.67 x 10⁵ seconds
= 2.67 x 10⁵ seconds / (60 seconds/minute) ≈ 4450 minutes.
Therefore, it takes approximately 4450 minutes for the light from the star to reach us.
6. The wavelength (λ) of an electromagnetic wave can be calculated using the formula: λ = c / f
where c is the speed of light and f is the frequency of the wave.
Frequency (f) = 10 Hz
Substituting the values into the equation, we have:
λ = (3 x 10⁸ m/s) / 10 Hz
λ = 3 x 10⁷ m
Therefore, the wavelength of the 10 Hz electromagnetic wave is 30 million meters (30,000 km).
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In the image a particle is ejected from the nucleus of an atom. If the nucleus increases in atomic number (Z -> Z+1) than the small particle ejected from the nucleus is one of a(n) _________ or _________. However had the particle ejected been a helium nuclei, we would classify this type of decay as being _______ decay.
The process of a particle being ejected from the nucleus of an atom is known as radioactive decay.
When the atomic number of the nucleus increases (Z → Z + 1) after this process, the small particle ejected from the nucleus is either an electron or a positron.
However, if the ejected particle had been a helium nucleus, the decay would be classified as alpha decay.
In alpha decay, the nucleus releases an alpha particle, which is a helium nucleus.
An alpha particle consists of two protons and two neutrons bound together.
When an alpha particle is released from the nucleus, the atomic number of the nucleus decreases by 2, and the mass number decreases by 4.
beta particle is a high-energy electron or positron that is released during beta decay.
When a nucleus undergoes beta decay, it releases a beta particle along with an antineutrino or neutrino.
The correct answer is that if the nucleus increases in atomic number (Z → Z + 1),
the small particle ejected from the nucleus is either an electron or a positron,
while if the particle ejected had been a helium nucleus,
the decay would be classified as alpha decay.
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Question 3 (1 point) Listen When heavy nuclei are bombarded with neutrons with the purpose of splitting them, this is called fission fusion artificial transmutation Onatural transmutation Question 4 (
The answer to the first question is
fission
. When heavy nuclei are
bombarded
with neutrons with the purpose of splitting them, the process is called fission.
Fission is a type of
nuclear reaction
in which the nucleus of an atom is split into two or more smaller nuclei, along with the release of a significant amount of energy. This process is often used in nuclear power plants to generate electricity.
The answer to the second question is not
provided
. Please provide the complete question or the required terms to answer.
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2. Two closeby speakers produce sound waves. One of the speakers vibrates at 400 Hz. What would be the frequency of the other speaker, which produces 10 Hz of beats? A. 10 Hz B. 390 Hz C. 410 Hz
Summary:
The frequency of the other speaker would be 390 Hz. When two closeby speakers produce sound waves, a phenomenon known as beats can occur. Beats are the periodic variations in the intensity or loudness of sound that result from the interference of two waves with slightly different frequencies.
Explanation:
In this case, if one speaker vibrates at 400 Hz and the beats have a frequency of 10 Hz, it means that the frequency of the other speaker is slightly different. The beat frequency is the difference between the frequencies of the two speakers. So, by subtracting the beat frequency of 10 Hz from the frequency of one speaker (400 Hz), we find that the frequency of the other speaker is 390 Hz.
To understand this concept further, let's delve into the explanation. When two sound waves with slightly different frequencies interact, they undergo constructive and destructive interference, resulting in a periodic variation in the amplitude of the resulting wave. This variation is what we perceive as beats. The beat frequency is equal to the absolute difference between the frequencies of the two sound waves. In this case, the given speaker has a frequency of 400 Hz, and the beat frequency is 10 Hz. By subtracting the beat frequency from the frequency of the given speaker (400 Hz - 10 Hz), we find that the frequency of the other speaker is 390 Hz. This frequency creates the interference pattern that produces the 10 Hz beat frequency when combined with the 400 Hz wave. Therefore, the correct answer is B. 390 Hz.
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A cylindrical metal wire at room temperature is carrying electric current between its ends. One end is at potential VA = 50V, and the other end is at potential VB = 0V . Rank the following actions in terms of the change that each one separately would produce in the current from the greatest increase to the greatest decrease. In your ranking, note any cases of equality.(a) Make VA = 150V with VB = 0V (b) Adjust VA to triple the power with which the wire converts electrically transmitted energy into internal energy.(c) Double the radius of the wire.(d) Double the length of the wire. (e) Double the Celsius temperature of the wire.
Ranking the actions in terms of the change they would produce in the current from greatest increase to greatest decrease would be: (a) Make VA = 150V with VB = 0V, (b) Adjust VA to triple the power, (c) Double the radius of the wire, (d) Double the Celsius temperature of the wire, (e) Double the length of the wire.
To rank the actions in terms of the change they would produce in the current, let's consider each one separately:
(a) Making VA = 150V with VB = 0V: This action would increase the potential difference between the ends of the wire, resulting in an increase in the current.
Since the resistance of the wire remains constant, Ohm's Law (V = IR) tells us that an increase in voltage would lead to an increase in current.
Therefore, this action would produce the greatest increase in the current.
(b) Adjusting VA to triple the power: This action does not directly affect the potential difference or resistance of the wire. Instead, it affects the power, which is given by P = IV.
If we triple the power, the current must increase since the potential difference remains constant. Therefore, this action would produce the second-greatest increase in the current.
(c) Doubling the radius of the wire: This action would increase the wire's cross-sectional area, resulting in a decrease in resistance. According to Ohm's Law, decreasing the resistance while keeping the potential difference constant would increase the current. Therefore, this action would produce a smaller increase in the current compared to the previous two actions.
(d) Doubling the length of the wire: This action would increase the wire's resistance. According to Ohm's Law, increasing the resistance while keeping the potential difference constant would decrease the current. Therefore, this action would produce a decrease in the current.
(e) Doubling the Celsius temperature of the wire: This action affects the wire's resistance. Generally, increasing the temperature of a metal wire increases its resistance. Therefore, doubling the temperature would increase the wire's resistance, resulting in a decrease in the current.
Ranking the actions in terms of the change they would produce in the current from greatest increase to greatest decrease would be: (a) Make VA = 150V with VB = 0V, (b) Adjust VA to triple the power, (c) Double the radius of the wire, (d) Double the Celsius temperature of the wire, (e) Double the length of the wire.
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Consider the vector A⃗ with components Ax= 2.00, Ay= 6.00, the vector B⃗ with components Bx = 2.00, By = -3.00, and the vector D⃗ =A⃗ −B
(1) Calculate the magnitude D of the vector D⃗. (Express your answer to three significant figures.)
(2) Calculate the angle theta that the vector D⃗ makes with respect to the positive x-x-axis.. (Express your answer to three significant figures.)
Part 1) The magnitude of vector D⃗ is approximately 6.32.
To calculate the magnitude of a vector, we use the formula:
|D⃗| = √(Dx² + Dy²)
Given that vector D⃗ = A⃗ - B⃗, we subtract the corresponding components:
Dx = Ax - Bx = 2.00 - 2.00 = 0.00
Dy = Ay - By = 6.00 - (-3.00) = 9.00
Substituting the values into the formula, we have:
|D⃗| = √(0.00² + 9.00²) ≈ 6.32
Therefore, the magnitude of vector D⃗ is approximately 6.32.
Part 2) The angle theta that vector D⃗ makes with respect to the positive x-axis is approximately 90.00 degrees.
To calculate the angle, we use the formula:
θ = atan(Dy / Dx)
Substituting the values we found earlier, we have:
θ = atan(9.00 / 0.00)
However, since Dx = 0.00, we have an undefined value for the angle using this formula. In this case, we can determine the angle by considering the signs of the components.
Since Dx = 0.00, the vector D⃗ lies entirely on the y-axis. The positive y-axis makes an angle of 90.00 degrees with the positive x-axis.
Therefore, the angle theta that vector D⃗ makes with respect to the positive x-axis is approximately 90.00 degrees.
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In figure 1 , two positive point charges +q and +2q are separated by a distance x. Figure 1. They are both held in place so that they cannot move. What is the direction of the electric forces they exert on one another? 2. Describe the magnitudes of the electric forces they exert on one another. 3. Explain why they exert these magnitudes on one another. 4. What would happen to the magnitudes of the electric forces if the two charges are separated by a distance 2x instead of x ?
The separation is doubled, the area that the electric field lines can spread out over is quadrupled, and hence the magnitude of the electric field, and therefore the force, is one-fourth as much.
1. The electric forces that two positive point charges +q and +2q exert on one another are opposite in direction to one another. Figure 1 illustrates that the direction of the force on +q due to +2q is in the direction of the +q charge, whereas the direction of the force on +2q due to +q is in the direction of the +2q charge.
2. The electric forces they exert on one another have equal magnitudes.3. The electric force acting on any point charge arises due to the electric field generated by other charges in the vicinity. Therefore, the magnitudes of the electric forces between charges are proportional to the magnitudes of the charges. In this case, since +2q is twice the magnitude of the +q charge, the magnitude of the electric force on +2q due to +q is twice that of the force on +q due to +2q. However, since the distance between the two charges is the same, the force on each charge has the same magnitude.
4. If the two charges are separated by a distance of 2x instead of x, the magnitude of the electric force between them decreases by a factor of 4 because the electric force is inversely proportional to the square of the distance between the charges. This is because, when the separation is doubled, the area that the electric field lines can spread out over is quadrupled, and hence the magnitude of the electric field, and therefore the force, is one-fourth as much.
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A planar loop consisting of your tums of wire, each of which encloses o 20 m, is oriented perpendicularly to a magnetic field that increases uniformly in magnitude from 70 mt to 18 mt in a time of 50 ms What is the resulting induced current in the coil if the total resistance of the coil is 5.0
The resulting induced current in the coil is approximately -0.208 A.
To determine the induced current in the coil, we can use Faraday's law of electromagnetic induction, which states that the induced electromotive force (emf) in a loop is equal to the rate of change of magnetic flux through the loop.
The magnetic flux through the loop can be calculated by multiplying the magnetic field strength by the area of the loop. In this case, the loop has an area of 20 m².
The rate of change of magnetic field can be found by taking the difference between the final and initial magnetic field strengths and dividing it by the time interval. In this case, the change in magnetic field is (18 mT - 70 mT) = -52 mT and the time interval is 50 ms, or 0.05 seconds.
Now, let's calculate the induced emf:
ΔΦ = ΔB * A = (-52 mT) * (20 m²) = -1040 mT*m²
Next, we need to convert the units to the standard SI unit, Tesla, by dividing by 1000:
ΔΦ = -1.04 T*m²
Finally, we can calculate the induced current using Ohm's law:
emf = I * R
Rearranging the equation, we have:
I = emf / R = (-1.04 T*m²) / (5.0 Ω)
Calculating the result, we get:
I = -0.208 A
The negative sign indicates that the current flows in the opposite direction to the conventional current flow convention.
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a six string guitar with a high E string had a mass per units length of 0.000309kg/m if the E string is plucked product a wave in the string at a speed of 427.23m/s .What is the tension generated so the string?.
The tension generated in the high E string of a six-string guitar, with a mass per unit length of 0.000309 kg/m, when plucked to produce a wave at a speed of 427.23 m/s, is approximately 56.2362 Newtons. Tension in the string is essential for producing the desired pitch and maintaining stability during vibration.
The tension in a string affects its wave behavior and pitch. In this case, we have a high E string on a six-string guitar with a known mass per unit length (linear mass density) of 0.000309 kg/m. When the string is plucked, it generates a wave with a speed of 427.23 m/s.
To find the tension, we can use the wave equation for a string:
v = √(T/μ)
where v is the wave velocity, T is the tension, and μ is the linear mass density. Rearranging the equation, we solve for T:
T = μ * v^2
Putting in the given values:
T = 0.000309 kg/m * (427.23 m/s)^2
Calculating the expression:
T ≈ 0.000309 kg/m * 182601.8529 m^2/s^2
T ≈ 56.2362 N
Therefore, the tension generated in the high E string of the guitar is approximately 56.2362 Newtons. This tension is crucial for producing the desired sound when the string is played and ensuring the stability of the string's vibrations.
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a) How do fins on surfaces enhance the rate of heat transfer? b) Under what circumstances would the addition of fins decrease the rate of heat transfer? c) Differentiate between fin effectiveness and fin efficiency
a) Fins on surfaces enhance the rate of heat transfer by increased surface area and conductivity. b) The circumstances would the addition of fins decrease the rate of heat transfer if there is a large temperature difference between the surface and the fluid. c) The different between fin effectiveness and fin efficiency is fin effectiveness is influenced by the geometry, fin efficiency depends on both the geometry and the thermal properties.
Fins are usually used in heat exchangers, radiators, and other similar devices where heat transfer is critical. They are designed to improve heat transfer by increasing the surface area over which heat can be transferred and by improving the fluid dynamics around the surface. Finned surfaces are particularly useful in situations where there is a large temperature difference between the fluid and the surface. The fins work to extract heat from the surface more efficiently, thus improving the overall heat transfer rate.
The addition of fins may decrease the rate of heat transfer if there is a large temperature difference between the surface and the fluid. This is because the fins may actually act as insulators, preventing the fluid from coming into contact with the surface and extracting heat from it. In addition, if the fins are too closely spaced, they can create a turbulent flow that can decrease the heat transfer rate. Therefore, the design of the fins is crucial in ensuring that they do not impede the heat transfer rate.
Fin effectiveness refers to the ability of a fin to increase the heat transfer rate of a surface. It is the ratio of the actual heat transfer rate with fins to the heat transfer rate without fins. Fin efficiency is the ratio of the heat transfer rate from the fin surface to the heat transfer rate from the entire finned surface. Fin effectiveness is influenced by the geometry of the fin, whereas fin efficiency depends on both the geometry and the thermal properties of the fin.
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X-rays of wavelength 0.116 nm reflect off a crystal and a second-order maximum is recorded at a Bragg angle of 22.1°. What is the spacing between the scattering planes in this crystal?
To determine the spacing between the scattering planes in the crystal, we can use Bragg's Law.
Bragg's Law relates the wavelength of X-rays, the angle of incidence (Bragg angle), and the spacing between the scattering planes.
The formula for Bragg's Law is: nλ = 2d sinθ
In this case, we are dealing with second-order diffraction (n = 2), and the wavelength of the X-rays is given as 0.116 nm. The Bragg angle is 22.1°.
We need to rearrange the equation to solve for the spacing between the scattering planes (d):
d = nλ / (2sinθ)
Plugging in the values:
d = (2 * 0.116 nm) / (2 * sin(22.1°))
≈ 0.172 nm
Therefore, the spacing between the scattering planes in the crystal is approximately 0.172 nm.
when X-rays with a wavelength of 0.116 nm are incident on the crystal, and a second-order maximum is observed at a Bragg angle of 22.1°, the spacing between the scattering planes in the crystal is approximately 0.172 nm.
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When the LR circuit resists success, he wonders. He wires
up the modified RLC circuit shown at the right using an AC
source.
What is the RMS voltage across the capacitor?
The RMS voltage across the capacitor in the modified RLC circuit can be calculated using the formula: Vc = (1/√2) * (Xc / √(R² + (Xl - Xc)²)), where Xc represents the reactance of the capacitor, Xl represents the reactance of the inductor, and R represents the resistance.
1. Determine the reactance of the capacitor (Xc) using the formula Xc = 1 / (2 * π * f * C), where f is the frequency of the AC source and C is the capacitance.
2. Calculate the reactance of the inductor (Xl) using the formula Xl = 2 * π * f * L, where L is the inductance of the inductor.
3. Find the total impedance (Z) of the circuit using the formula Z = √(R² + (Xl - Xc)²), where R is the resistance.
4. Calculate the RMS voltage across the capacitor (Vc) using the formula Vc = (1/√2) * (Xc / Z).
5. Substitute the values of Xc, Xl, and R into the formulas and calculate the RMS voltage across the capacitor.
By following these steps, you can determine the RMS voltage across the capacitor in the modified RLC circuit.
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Burl and Paul have a total weight of 688 N. The tensions in the ropes that support the scaffold they stand on add to 1448 N. Determine the weight of the scaffold (N). (Note: Be sure to report answer with the abbreviated form of the unit.)
The weight of the scaffold is 1208 N.
Given Data: Burl and Paul have a total weight of 688 N.
Tensions in the ropes that support the scaffold they stand on add to 1448 N.
Formula Used: The weight of the scaffold can be calculated by using the formula given below:
Weight of the Scaffold = Tension on Left + Tension on Right - Total Weight of Burl and Paul
Weight of the Scaffold = Tension L + Tension R - (Burl + Paul)
So the weight of the scaffold is 1208 N. (Note: Be sure to report answer with the abbreviated form of the unit.)
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We wish to coat flat glass (n 1.50) with a transparent material (n = 1.25) so that reflection of light at wavelength 600 nm is eliminated by interference. What minimum thick- ness can the coating have to do this?
The minimum thickness of the transparent coating needed to eliminate reflection of light at a wavelength of 600 nm through interference is approximately 120 nm.
To determine the minimum thickness, we can use the formula for the phase change upon reflection from an interface:
2nt = mλ
Where:
n is the refractive index of the medium (transparent coating),
t is the thickness of the coating,
m is an integer representing the order of interference (in this case, we want to eliminate reflection, so m = 0), and
λ is the wavelength of light.
Since we want to eliminate reflection, the phase change upon reflection should be zero. Therefore, we can rearrange the equation to solve for the minimum thickness of the coating:
t = (mλ) / (2n)
Substituting the given values into the formula, we find that the minimum thickness required for the coating is approximately 120 nm.
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1. Explain the following: 1.1) What is meant by anaerobic treatment process characteristics? 1.2) How many stages are in anaerobic digestion mechanism? 1.3) What is the main purpose of Upflow Anaerobic Sludge Blanket (UASB) system? 1.4) What will happen if the world goes past 1.5 degrees of global warming? 1.5) Give advantages of UV. 1.6) When the Fenton's reagent reacts with a wastewater, what products get produced?
1.1) Anaerobic treatment process characteristics refer to the specific attributes and conditions associated with the treatment of wastewater or organic matter in the absence of oxygen.
1.2) The anaerobic digestion mechanism typically involves four stages: hydrolysis, acidogenesis, acetogenesis, and methanogenesis.
1.3) The main purpose of an Upflow Anaerobic Sludge Blanket (UASB) system is to efficiently treat wastewater by utilizing the anaerobic digestion process.
1.4) If the world goes past 1.5 degrees of global warming, it would have significant and far-reaching consequences for the environment and human well-being.
1.5) Ultraviolet (UV) radiation offers advantages such as chemical-free disinfection and versatility in various applications.
1.6) When Fenton's reagent reacts with wastewater, it produces hydroxyl radicals and other reactive oxygen species, leading to the degradation of organic pollutants.
1.1) Anaerobic treatment process characteristics refer to the specific attributes and conditions associated with the treatment of wastewater or organic matter in the absence of oxygen. These characteristics include the use of anaerobic microorganisms, the production of biogas (mainly methane), and the conversion of organic substances into simpler compounds through a series of biochemical reactions.
1.2) The anaerobic digestion mechanism typically involves four stages: hydrolysis, acidogenesis, acetogenesis, and methanogenesis. In the hydrolysis stage, complex organic matter is broken down into simpler compounds. In the acidogenesis stage, acidogenic bacteria convert the products of hydrolysis into volatile fatty acids. Acetogenesis follows, where acetogenic bacteria further break down the fatty acids into acetate, hydrogen, and carbon dioxide. Finally, methanogenic archaea convert these compounds into methane and carbon dioxide in the methanogenesis stage.
1.3) The main purpose of an Upflow Anaerobic Sludge Blanket (UASB) system is to treat wastewater by utilizing the anaerobic digestion process. The UASB system is designed to efficiently separate and retain the anaerobic sludge biomass in the reactor, allowing for the digestion of organic matter and the conversion of volatile fatty acids into biogas. This system is commonly used for high-strength wastewater treatment, such as industrial or municipal wastewater, as it provides effective removal of organic pollutants while producing biogas as a valuable byproduct.
1.4) If the world goes past 1.5 degrees of global warming, it would have significant and far-reaching consequences for the environment, ecosystems, and human well-being. The impacts would include more frequent and severe heatwaves, rising sea levels, intensified storms and hurricanes, disruptions to ecosystems and biodiversity, and increased risks to food security and water resources. It would also exacerbate the existing challenges of climate change, making it harder to mitigate its effects and adapt to the changes. Efforts to limit global warming to 1.5 degrees Celsius are aimed at minimizing these potential consequences and preserving a sustainable and habitable planet for future generations.
1.5) Ultraviolet (UV) radiation has several advantages in various applications. In water treatment, UV disinfection is a chemical-free method that effectively inactivates microorganisms, including bacteria, viruses, and protozoa, without adding harmful byproducts to the water. UV treatment is efficient, environmentally friendly, and does not alter the taste, odor, or color of the water. Moreover, UV radiation can be applied in a wide range of industries, including drinking water treatment, wastewater treatment, pharmaceutical manufacturing, and food processing, making it a versatile and reliable technology for microbial control.
1.6) When Fenton's reagent reacts with wastewater, it produces hydroxyl radicals (•OH) and other reactive oxygen species. Fenton's reagent consists of a combination of hydrogen peroxide (H2O2) and a ferrous iron (Fe2+) catalyst. The hydroxyl radicals generated by this reaction are highly reactive and can oxidize and degrade various organic pollutants present in the wastewater. The •OH radicals attack and break down organic compounds, leading to the degradation of contaminants and the formation of simpler, less toxic byproducts. Fenton's reagent is commonly used as an advanced oxidation process for the treatment of wastewater containing persistent organic pollutants.
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An elastic cord is 55 cm long when a weight of 79 N hangs from it but is 84 cm long when a weight of 220 N hangs from it. Part A What is the "spring" constant k of this elastic cord? Express your answer to two significant figures and include the appropriate units.
An elastic cord is 55 cm long when a weight of 79 N hangs from it but is 84 cm long when a weight of 220 N hangs from it. the spring constant (k) of the elastic cord is approximately 5.17 N/cm.
To find the spring constant (k) of the elastic cord, we can use Hooke's Law, which states that the force applied to an elastic material is directly proportional to the extension or compression of the material.
In this case, we have two sets of data:
When a weight of 79 N hangs from the cord, the length is 55 cm.
When a weight of 220 N hangs from the cord, the length is 84 cm.
Let's denote the original length of the cord as L₀, the extension in the first case as x₁, and the extension in the second case as x₂.
According to Hooke's Law, we have the following relationship:
F = k * x,
where F is the force applied, x is the extension or compression, and k is the spring constant.
In the first case:
79 N = k * x₁.
In the second case:
220 N = k * x₂.
We can rearrange these equations to solve for k:
k = 79 N / x₁,
k = 220 N / x₂.
To find the spring constant (k), we need to calculate the average value of k using the two sets of data:
k = (79 N / x₁ + 220 N / x₂) / 2.
Now, let's calculate the value of k:
k = (79 N / (84 cm - 55 cm) + 220 N / (84 cm - 55 cm)) / 2.
k = (79 N / 29 cm + 220 N / 29 cm) / 2.
k = (79 N + 220 N) / (29 cm * 2).
k = 299 N / (58 cm).
k ≈ 5.17 N/cm.
Rounded to two significant figures, the spring constant (k) of the elastic cord is approximately 5.17 N/cm.
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If an apple that is dropped from an altitude of 100 m reaches an altitude of 80 m after falling for t = 2 seconds, what altitude will it be at in t = t = 4 seconds?
The apple will be at an altitude of approximately 178.4 meters at 4 seconds.
To determine the altitude of the apple at t = 4 seconds, we can use the equation of motion for free fall:
h = h0 + v0t + (1/2)gt²
where:
h is the final altitude,
h0 is the initial altitude,
v0 is the initial velocity (which is 0 m/s since the apple is dropped),
g is the acceleration due to gravity (approximately 9.8 m/s²),
t is the time.
Initial altitude (h0) = 100 m
Time (t) = 4 seconds
Substituting the values into the equation:
h = h0 + v0t + (1/2)gt²
Since the apple is dropped, the initial velocity (v0) is 0 m/s:
h = h0 + 0×t + (1/2)gt²
h = h0 + (1/2)gt²
Using the given values:
h = 100 + (1/2)9.8(4)²
h = 100 + 0.59.816
h = 100 + 78.4
h = 178.4 m
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A certain rod is moving in a magnetic field. The length of the rod is 1.50 m, and its speed is 3.20 m/s, whereas the field strength is 0.640 T. The magnetic field is perpendicular to the velocity of the rod, and both are perpendicular to the length-axis. What is the voltage drop across this rod, in V?
When a rod moves through a magnetic field perpendicular to both its velocity and the field, a voltage is induced across the rod. The voltage drop across the rod is 3.072 volts.
In this case, with a rod length of 1.50 m, a velocity of 3.20 m/s, and a magnetic field strength of 0.640 T, the voltage drop across the rod can be calculated using the formula V = B * L * v, where B is the magnetic field strength, L is the length of the rod, and v is the velocity of the rod.
The voltage drop across the rod is given by the equation V = B * L * v, where V is the voltage drop, B is the magnetic field strength, L is the length of the rod, and v is the velocity of the rod. In this case, the length of the rod (L) is 1.50 m, the velocity (v) is 3.20 m/s, and the magnetic field strength (B) is 0.640 T.
Plugging in these values into the equation, we have V = (0.640 T) * (1.50 m) * (3.20 m/s). Multiplying these values, we get V = 3.072 V. Therefore, the voltage drop across the rod is 3.072 volts.
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A beam of protons is moving toward a target in a particle accelerator. This beam constitutes a current whose value is 0.73μA. (a) How many protons strike the target in 20 seconds? (b) Each proton has a kinetic energy of 5.3×10^ −12 J. Suppose the target is a 18-gram block of metal whose specific heat capacity is 1300 J/(kgC ∘ ), and all the kinetic energy of the protons goes into heating it up. What is the change in temperature of the block at the end of 20 s?
To solve this problem, we need to calculate the number of protons that strike the target in 20 seconds and then determine the change in temperature of the block when all the kinetic energy of the protons is transferred to it.
(a) How many protons strike the target in 20 seconds?
Given:
Current = 0.73 μA
Time = 20 seconds
To find the number of protons, we need to use the equation:
Q = I * t
Where Q is the charge, I is the current, and t is the time.
The charge of a proton is e = 1.6 x 10^-19 C.
Q = (0.73 x 10^-6 A) * (20 s)
Q = 1.46 x 10^-5 C
The number of protons is equal to the total charge divided by the charge of a single proton:
Number of protons = Q / e
Number of protons = (1.46 x 10^-5 C) / (1.6 x 10^-19 C)
Number of protons ≈ 9.13 x 10^13 protons
Therefore, approximately 9.13 x 10^13 protons strike the target in 20 seconds.
(b) Now, let's calculate the change in temperature of the block when all the kinetic energy of the protons is transferred to it.
Given:
Mass of the block (m) = 18 g = 0.018 kg
Specific heat capacity (c) = 1300 J/(kg⋅°C)
Kinetic energy of each proton (KE) = 5.3 x 10^-12 J
Time (t) = 20 s
The total energy transferred to the block is equal to the total kinetic energy of the protons:
Total energy = Number of protons * Kinetic energy of each proton
Total energy = (9.13 x 10^13) * (5.3 x 10^-12 J)
The change in temperature (ΔT) can be calculated using the equation:
Total energy = m * c * ΔT
ΔT = Total energy / (m * c)
ΔT = [(9.13 x 10^13) * (5.3 x 10^-12 J)] / [(0.018 kg) * (1300 J/(kg⋅°C))]
Calculating the value:
ΔT ≈ 2.20 x 10^9 °C
Therefore, the change in temperature of the block at the end of 20 seconds is approximately 2.20 x 10^9 degrees Celsius.
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Question 20 of 26 < > -/3 ili : View Policies Current Attempt in Progress In a circus act, a 67 kg clown is shot from a cannon with an initial velocity of 15 m/s at some unknown angle above the horizontal. A short time later the clown lands in a net that is 4.1 m vertically above the clown's initial position. Disregard air drag. What is the kinetic energy of the clown as he lands in the net? Number Units
The kinetic energy of the clown as he lands in the net is approximately 9,446.25 Joules.
To calculate the kinetic energy of the clown as he lands in the net, we need to consider the change in potential energy and the conservation of mechanical energy. Since the clown lands in a net that is 4.1 m vertically above his initial position, we can calculate the change in potential energy:
ΔPE = m * g * h
Where ΔPE is the change in potential energy, m is the mass of the clown (67 kg), g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the vertical distance traveled (4.1 m).
ΔPE = 67 kg * 9.8 m/s² * 4.1 m
ΔPE ≈ 2709.34 Joules
Since there is no air drag and no change in mechanical energy during the clown's flight, the kinetic energy at landing is equal to the initial kinetic energy:
KE_initial = KE_final
The initial kinetic energy can be calculated using the formula:
KE = 0.5 * m * v²
Where KE is the kinetic energy, m is the mass of the clown (67 kg), and v is the initial velocity of the clown (15 m/s).
KE_initial = 0.5 * 67 kg * (15 m/s)²
KE_initial ≈ 7594.91 Joules
Therefore, the kinetic energy of the clown as he lands in the net is approximately 9,446.25 Joules.
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Question Completion Status QUESTION 3 1 points In the Wheatstone Bridge experiment, three students try to find the unknow resistance Rx by studying the variation of L2 versus R9"l1 as shown in the following graph: L 1 N R*L, Question Completion Status: • RL, where I RER Use the given graph and the relation to decide which student has lowest value of Rx? *L
In the Wheatstone Bridge experiment, three students try to find the unknown resistance Rx by studying the variation of L2 versus R9"l1, as shown in the following graph: L 1 N R*L, Question Completion Status:
• RL, where I RER. The three students are represented in different colors on the graph, and they obtained different values of R9 and L2. From the graph, the student who has the lowest value of Rx is the one whose line passes through the origin, since this means that R9 is equal to zero.
The equation of the line that passes through the origin is L2 = m * R9, where m is the slope of the line. For the blue line, m = 4, which means that Rx = L1/4 = 20/4 = 5 ohms. For the green line, m = 2, which means that Rx = L1/2 = 20/2 = 10 ohms. For the red line, m = 3, which means that Rx = L1/3 = 20/3 6.67 ohms. Therefore, the student who has the lowest value of Rx is the one whose line passes through the origin, which is the blue line, and the value of Rx for this student is 5 ohms.
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During beta decay, a neutron changes into a proton and a(n) electron positron nucleon quark Listen The bombardment of a stable isotope to force it to decay is called fusion natural transmutation artificial transmutation fission
During beta decay, a neutron changes into a proton and an electron. The bombardment of a stable isotope to force it to decay is called
artificial transmutation
.
Beta decay is a radioactive decay process that occurs when a neutron converts into a proton and an electron.
It results in the nucleus emitting a
high-speed electron
(beta particle), and the atomic number of the atom increases by one while the mass number remains the same.Artificial transmutation is a process that involves bombarding an atom's nucleus with high-energy particles, which causes it to undergo a nuclear reaction. By doing so, the nucleus of an atom can be changed artificially.
The
bombardment
of a stable isotope to force it to decay is known as artificial transmutation.Fusion, fission, and natural transmutation are other nuclear processes, which are different from artificial transmutation. In fusion, two atomic nuclei come together to form a new, heavier nucleus, which is accompanied by the release of energy. In fission, a heavy nucleus is split into two smaller nuclei, with the release of energy. Natural transmutation occurs when a nucleus decays on its own due to the instability of the nucleus.
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3. An object(16kg) that is moving at 12.5m/s to the West makes an elastic head-on collision with another object(14kg) that is moving to the East at 16 m/s. After the collision, the second object moves to the West with a velocity of 14.4m/s. A. Find the velocity of the first object after the collision. B. What is the kinetic energy after the collision?
The velocity of the first object after the collision is 14.1 m/s, and the kinetic energy after the collision is 1590.48 J.
To solve this problem, we can apply the principles of conservation of momentum and conservation of kinetic energy.
Let's denote the velocity of the first object (16 kg) before the collision as V1 and the velocity of the second object (14 kg) before the collision as V2. After the collision, the velocity of the first object is denoted as V1' and the velocity of the second object is denoted as V2'.
Using the conservation of momentum, we have:
(mass1 * V1) + (mass2 * V2) = (mass1 * V1') + (mass2 * V2')
Substituting the given values:
(16 kg * (-12.5 m/s)) + (14 kg * (16 m/s)) = (16 kg * V1') + (14 kg * (-14.4 m/s))
Simplifying the equation, we find:
-200 kg m/s + 224 kg m/s = 16 kg * V1' - 201.6 kg m/s
Combining like terms:
24 kg m/s = 16 kg * V1' - 201.6 kg m/s
Adding 201.6 kg m/s to both sides:
24 kg m/s + 201.6 kg m/s = 16 kg * V1'
225.6 kg m/s = 16 kg * V1'
Dividing both sides by 16 kg:
V1' = 14.1 m/s (velocity of the first object after the collision)
To calculate the kinetic energy after the collision, we use the formula:
Kinetic Energy = (1/2) * mass * velocity^2
Kinetic Energy1' = (1/2) * 16 kg * (14.1 m/s)^2
Kinetic Energy1' = 1/2 * 16 kg * 198.81 m^2/s^2
Kinetic Energy1' = 1/2 * 3180.96 J
Kinetic Energy1' = 1590.48 J
Therefore, the velocity of the first object after the collision is 14.1 m/s, and the kinetic energy after the collision is 1590.48 J.
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1. Find the capacitance of the spherical capacitor of inner radius ( 4 cm) and outer radius ( 8 cm). Select one: a. 14.82 PF b. 2.97 PF C. 26.69 PE d. 8.9 PF
The correct option is b. 2.97 pF.
The capacitance of the spherical capacitor of inner radius 4 cm and outer radius 8 cm can be calculated using the formula;
C = 4πε (ab / a+b)
where,
a is the radius of the inner sphere,
b is the radius of the outer sphere, and
ε is the permittivity of free space which is 8.85 x 10-12 F/m.
Therefore, substituting the given values into the above formula,
we have;
C = 4πε (ab / a+b)
C = 4 × 3.142 × 8.85 × 10-12 (4 × 8 × 10-2 / 4 + 8 × 10-2)
C = 2.97 pF
Therefore, the capacitance of the spherical capacitor of inner radius 4 cm and outer radius 8 cm is 2.97 pF.
Hence, the correct option is b. 2.97 pF.
Note that the charge (Q) on a capacitor is determined by Q = CV,
where V is the voltage applied across the plates of the capacitor.
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A coiled telephone cord forms a spiral with 62.0 turns, a diameter of 1.30 cm, and an unstretched length of 62.0 cm.
Determine the inductance of one conductor in the unstretched cord.
The inductance of one conductor in the unstretched cord is approximately 1.83 × 10^(-7) H (Henrys). This value is calculated using the formula for inductance, taking into account the number of turns, cross-sectional area, and length of the solenoid .
The inductance of one conductor in the unstretched cord can be determined as follows: The self-inductance L of a long, thin solenoid (narrow coil of wire) can be calculated using the following formula: L = μ₀n²πr²lwhere:μ₀ = 4π x 10-7 T m A⁻¹n = number of turns per unit lengthr = radiusl = length of the solenoidTaking one conductor of the coiled telephone cord as the solenoid, L = μ₀n²πr²lThe radius r is half of the diameter, r = d/2L = μ₀n²π(d/2)²lWhere n = Number of turns / Length of cord = 62/0.62 m = 100 turns/meter. Substituting the values of the given parameters, we get: L = μ₀ × (100 turns/m)² × π × (1.30 cm / 2)² × 0.62 mL = 1.37 x 10⁻⁶ H or 1.37 µH Therefore, the inductance of one conductor in the unstretched cord is 1.37 µH.
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