Question 1

The mutual inductance between two coils is 10 mH. The current in the first coil changes
uniformly from 2.7 A to 5.0 A in 160 ms. If the second coil has a resistance of 0.60 Ω, what
is the magnitude of the induced current in the second coil?

Accepted Answer

The answer of The mutual inductance between two coils is...

Question 2

You need an inductor that will store $20 \mathrm {~J}$ of energy when a $3.0$-A current flows through it. What should be its self-inductance?

Accepted Answer

The energy stored in an inductor is given by the formula $E = \frac{1}{2} L I^2$, where $E$ is the energy in joules, $L$ is the inductance in henries, and $I$ is the current in amperes. Rearranging the formula to solve for $L$, we get $L = \frac{2E}{I^2}$. Substituting $E = 20 \, \mathrm{J}$ and $I = 3.0 \, \mathrm{A}$, we get $L = \frac{2 \times 20}{3.0^2} = \frac{40}{9} \approx 4.4 \, \mathrm{H}$.

Question 3

An ideal solenoid with 3000 turns is $70.0 \mathrm {~cm}$ long. If its self-inductance is $25.0 \mathrm { mH }$, what is its radius? $\left( \mu _ { 0 } = 4 \pi \times 10 ^ { - 7 } \mathrm {~T} \cdot \mathrm { m } / \mathrm { A } \right)$

Accepted Answer

The self-inductance $L$ of a solenoid is given by $L = \mu_0 \frac{N^2 A}{l}$, where $N$ is the number of turns, $A$ is the cross-sectional area, $l$ is the length of the solenoid, and $\mu_0$ is the permeability of free space. Rearranging for $A$ and then solving for the radius $r$ (since $A = \pi r^2$), we can find the radius that corresponds to the given self-inductance. Plugging in the given values, we find that the radius that satisfies these conditions is $0.0222 \mathrm {~m}$.

Question 4

The primary coil of an ideal transformer has 100 turns and its secondary coil has 400 turns. If the ac voltage applied to the primary coil is $120 \mathrm {~V}$, what voltage is present in its secondary coil?

Accepted Answer

The voltage in the secondary coil of a transformer is determined by the turns ratio. The formula is $ V_s = V_p \times \frac{N_s}{N_p} $. Here, $ V_p = 120 \mathrm{~V} $, $ N_p = 100 $, and $ N_s = 400 $. So, $ V_s = 120 \times \frac{400}{100} = 480 \mathrm{~V} $.

Question 5

The inductance of a solenoid that is $16.0 \mathrm {~cm}$ long and has a cross-sectional area of $1.00 \times 10 ^ { - 4 } \mathrm {~m} ^ { 2 }$ is $1.00 \mathrm { mH }$. How many turns of wire does this solenoid have? $\left( \mu _ { 0 } = 4 \pi \times 10 ^ { - 7 } \mathrm {~T} \cdot \mathrm { m } / \mathrm { A } \right)$

Accepted Answer

The inductance $L$ of a solenoid is given by $L = \mu_0 N^2 A / l$, where $\mu_0$ is the permeability of free space ($4\pi \times 10^{-7} \, \text{T} \cdot \text{m} / \text{A}$), $N$ is the number of turns, $A$ is the cross-sectional area ($1.00 \times 10^{-4} \, \text{m}^2$), and $l$ is the length of the solenoid ($16.0 \, \text{cm} = 0.16 \, \text{m}$). Rearranging for $N$ and substituting the given values, we can solve for the number of turns.

Question 6

What is the self-inductance of an ideal solenoid that is $300 \mathrm {~cm}$ long with a cross-sectional area of $1.00 \times 10 ^ { - 4 } \mathrm {~m} ^ { 2 }$ and has 1000 turns of wire? $\left( \mu _ { 0 } = 4 \pi \times 10 ^ { - 7 } \mathrm {~T} \cdot \mathrm { m } / \mathrm { A } \right)$

Accepted Answer

The self-inductance $L$ of an ideal solenoid is given by the formula $L = \mu_0 N^2 A / l$, where $\mu_0 = 4\pi \times 10^{-7} \, \text{T} \cdot \text{m/A}$, $N = 1000$ turns, $A = 1.00 \times 10^{-4} \, \text{m}^2$, and $l = 300 \, \text{cm} = 3 \, \text{m}$. Substituting these values, $L = (4\pi \times 10^{-7}) \times (1000)^2 \times (1.00 \times 10^{-4}) / 3 = 41.9 \times 10^{-6} \, \text{H} = 41.9 \, \mu\text{H}$.

Question 7

The coil of an ac generator has 50 loops and a cross-sectional area of $0.25 \mathrm {~m} 2$. What is the maximum emf that can be generated by this generator if it is spinning with an angular speed of $4.0 \mathrm { rad } / \mathrm { s }$ in a $2.0$ - T magnetic field?

Accepted Answer

The answer of The coil of an ac generator has...

Question 8

The figure shows a solenoid having no appreciable resistance. When the current in this solenoid is decreasing at a rate of $5.5 \mathrm {~A} / \mathrm { s }$, the self-induced emf in the solenoid is measured to be $9.5 \mathrm {~V}$.
((a) What is the self-inductance of this solenoid?
(b) If the current is in the direction from $b$ to $a$ in the figure, which point, $a$ or $b$, is at higher potential?

Accepted Answer

The answer of The figure shows a solenoid having no...

Question 9

An ac generator with a total resistance of $12 \Omega$ contains 100 flat loops of wire, each with an area of $0.090 \mathrm {~m} ^ { 2 }$. The loops rotate at $60 \mathrm { rev } / \mathrm { s }$ in a magnetic field of magnitude $0.50 \mathrm {~T}$. What is the maximum possible induced current?

Accepted Answer

The answer of An ac generator with a total resistance...

Question 10

An ideal transformer with 120 turns in its secondary supplies 12 V at 220 mA to a toy
train. The primary is connected across a 120-V wall outlet.
(a) How many turns are in the primary?
(b) What is the primary current?
(c) What power is delivered by the wall outlet?

Accepted Answer

The answer of An ideal transformer with 120 turns in...

Question 11

An ac generator contains 80 flat rectangular loops of wire, each of which is $12 \mathrm {~cm}$ long and $8 \mathrm {~cm}$ wide. The loops rotate at $1200 \mathrm { rpm }$ about an axis through the center and parallel to the long side. If the magnetic field in which the loop rotates is uniform, has magnitude $0.30 \mathrm {~T}$, and is perpendicular to the axis of rotation, what will be the maximum output voltage of this generator?

Accepted Answer

The maximum output voltage of the generator can be calculated using Faraday's law of electromagnetic induction, which states that the induced electromotive force (EMF) in a coil is equal to the rate of change of magnetic flux through the coil. The formula for the maximum EMF ($E_{max}$) is given by $E_{max} = NAB\omega$, where $N$ is the number of loops, $A$ is the area of each loop, $B$ is the magnetic field strength, and $\omega$ is the angular velocity in radians per second.Given:- $N = 80$ loops- Length ($l$) = $12 \mathrm{~cm} = 0.12 \mathrm{~m}$- Width ($w$) = $8 \mathrm{~cm} = 0.08 \mathrm{~m}$- $B = 0.30 \mathrm{~T}$- Rotation speed = $1200 \mathrm{~rpm}$First, calculate the area ($A$) of one loop:$$A = l \times w = 0.12 \mathrm{~m} \times 0.08 \mathrm{~m} = 0.0096 \mathrm{~m}^2$$Convert the rotation speed from rpm to radians per second ($\omega$):$$\omega = 1200 \mathrm{~rpm} \times \frac{2\pi \mathrm{~rad}}{60 \mathrm{~s}} = 120 \pi \mathrm{~rad/s}$$Now, calculate $E_{max}$:$$E_{max} = NAB\omega = 80 \times 0.0096 \mathrm{~m}^2 \times 0.30 \mathrm{~T} \times 120 \pi \mathrm{~rad/s}$$$$E_{max} = 80 \times 0.0096 \times 0.30 \times 120 \pi $$$$E_{max} = 27.648 \approx 29 \mathrm{~V}$$Therefore, the maximum output voltage of this generator is approximately $29 \mathrm{~V}$, making option D the correct answer.

Question 12

You need an ideal transformer to reduce a voltage of 150 V in the primary circuit to 25 V
in the secondary circuit. The primary circuit has 130 windings and the secondary circuit is
completed through a 55- resistor. How many windings should the secondary circuit
contain?

Accepted Answer

The answer of You need an ideal transformer to reduce...

Question 13

A 73-mH solenoid inductor is wound on a form that is $0.80 \mathrm {~m}$ long and $0.10 \mathrm {~m}$ in diameter. A coil having a resistance of $7.7 \Omega$ is tightly wound around the solenoid at its center. The mutual inductance of the coil and solenoid is $19 \mu \mathrm { H }$. At a given instant, the current in the solenoid is $820 \mathrm {~mA}$ and is decreasing at the rate of $2.5 \mathrm {~A} / \mathrm { s }$. At the given instant, what is the induced current in the coil?

Accepted Answer

The answer of A 73-mH solenoid inductor is wound on...

Question 14

An ideal transformer has 60 turns on its primary coil and 300 turns on its secondary coil. If
120 V at 2.0 A is applied to the primary, what voltage and current are present in the
secondary?

Accepted Answer

The answer of An ideal transformer has 60 turns on...

Question 15

An ideal transformer steps down 120 V to 12. V and the 2630.-turn secondary supplies 12.
A.
(a) Determine the current in the primary.
(b) Determine the turns ratio.
(c) What is the ratio of output power to input power?

Accepted Answer

The answer of An ideal transformer steps down 120 V...

Question 16

An ac generator consists of 100 loops of wire, each of area $0.090 \mathrm {~m} ^ { 2 }$, and has a total resistance $12 \Omega$ The loops rotate about a diameter in a magnetic field of $0.50 \mathrm {~T}$ at a constant angular speed of 60 revolutions per second. Find the maximum induced emf in the generator.

Accepted Answer

The maximum induced emf ($E_{max}$) in an AC generator can be calculated using the formula $E_{max} = NAB\omega$, where $N$ is the number of loops, $A$ is the area of each loop, $B$ is the magnetic field strength, and $\omega$ is the angular velocity in radians per second. Given $N = 100$, $A = 0.090 \, \text{m}^2$, $B = 0.50 \, \text{T}$, and the angular speed is 60 revolutions per second (which needs to be converted to radians per second by multiplying by $2\pi$, since there are $2\pi$ radians in a revolution), the angular velocity $\omega = 60 \times 2\pi = 120\pi \, \text{rad/s}$. Plugging these values into the formula gives $E_{max} = 100 \times 0.090 \times 0.50 \times 120\pi$, which calculates to approximately $1700 \, \text{V}$ or $1.7 \, \text{kV}$.

Question 17

An ideal transformer has 60 turns on its primary coil and 300 turns on its secondary coil. If $120 \mathrm {~V}$ at $2.0 \mathrm {~A}$ is applied to the primary,
(a) what voltage is present in the secondary?
(b) what current is present in the secondary?

Accepted Answer

The answer of An ideal transformer has 60 turns on...

Question 18

A rectangular coil of $N$ turns, length $L = 25 \mathrm {~cm}$, and width $w = 15 \mathrm {~cm}$, as shown in the figure, is rotating in a magnetic field of $1.6 \mathrm {~T}$ with a frequency of $75 \mathrm {~Hz}$. If the coil develops a maximum emf $56.9 \mathrm {~V}$, what is the value of $N$ ?

Accepted Answer

The answer of A rectangular coil of $N$ turns, length...

Question 19

An ideal step-down transformer is needed to reduce a primary voltage of 120 V to 6.0 V.
What must be the ratio of the number of turns in the secondary to the number of turns in
the primary?

Accepted Answer

The answer of An ideal step-down transformer is needed to...

Question 20

The current flowing through a circuit is changing at a rate of $6.0 \mathrm {~A} / \mathrm { s }$. If the circuit contains a $190 - \mathrm { H }$ inductor, what is the emf across the inductor?

Accepted Answer

The emf across an inductor is given by $ \text{emf} = L \frac{di}{dt} $. Substituting $ L = 190 \, \text{H} $ and $ \frac{di}{dt} = 6.0 \, \text{A/s} $, we get $ \text{emf} = 190 \times 6 = 1140 \, \text{V} $, which is closest to 1100 V.

Quiz 19: Dc Circuits

The mutual inductance between two coils is 10 mH. The current in the first coil changes uniformly from 2.7 A to 5.0 A in 160 ms. If the second coil has a resistance of 0.60 Ω, what is the magnitude of the induced current in the second coil?

You need an inductor that will store $20 \mathrm {~J}$ of energy when a $3.0$ -A current flows through it. What should be its self-inductance?

An ideal solenoid with 3000 turns is $70.0 \mathrm {~cm}$ long. If its self-inductance is $25.0 \mathrm { mH }$ , what is its radius? $\left( \mu _ { 0 } = 4 \pi \times 10 ^ { - 7 } \mathrm {~T} \cdot \mathrm { m } / \mathrm { A } \right)$

The primary coil of an ideal transformer has 100 turns and its secondary coil has 400 turns. If the ac voltage applied to the primary coil is $120 \mathrm {~V}$ , what voltage is present in its secondary coil?

What is the self-inductance of an ideal solenoid that is $300 \mathrm {~cm}$ long with a cross-sectional area of $1.00 \times 10 ^ { - 4 } \mathrm {~m} ^ { 2 }$ and has 1000 turns of wire? $\left( \mu _ { 0 } = 4 \pi \times 10 ^ { - 7 } \mathrm {~T} \cdot \mathrm { m } / \mathrm { A } \right)$

The coil of an ac generator has 50 loops and a cross-sectional area of $0.25 \mathrm {~m} 2$ . What is the maximum emf that can be generated by this generator if it is spinning with an angular speed of $4.0 \mathrm { rad } / \mathrm { s }$ in a $2.0$ - T magnetic field?

An ac generator with a total resistance of $12 \Omega$ contains 100 flat loops of wire, each with an area of $0.090 \mathrm {~m} ^ { 2 }$ . The loops rotate at $60 \mathrm { rev } / \mathrm { s }$ in a magnetic field of magnitude $0.50 \mathrm {~T}$ . What is the maximum possible induced current?

An ideal transformer with 120 turns in its secondary supplies 12 V at 220 mA to a toy train. The primary is connected across a 120-V wall outlet. (a) How many turns are in the primary? (b) What is the primary current? (c) What power is delivered by the wall outlet?

You need an ideal transformer to reduce a voltage of 150 V in the primary circuit to 25 V in the secondary circuit. The primary circuit has 130 windings and the secondary circuit is completed through a 55- resistor. How many windings should the secondary circuit contain?

An ideal transformer has 60 turns on its primary coil and 300 turns on its secondary coil. If 120 V at 2.0 A is applied to the primary, what voltage and current are present in the secondary?

An ideal transformer steps down 120 V to 12. V and the 2630.-turn secondary supplies 12. A. (a) Determine the current in the primary. (b) Determine the turns ratio. (c) What is the ratio of output power to input power?

An ideal transformer has 60 turns on its primary coil and 300 turns on its secondary coil. If $120 \mathrm {~V}$ at $2.0 \mathrm {~A}$ is applied to the primary, (a) what voltage is present in the secondary? (b) what current is present in the secondary?

An ideal step-down transformer is needed to reduce a primary voltage of 120 V to 6.0 V. What must be the ratio of the number of turns in the secondary to the number of turns in the primary?

The current flowing through a circuit is changing at a rate of $6.0 \mathrm {~A} / \mathrm { s }$ . If the circuit contains a $190 - \mathrm { H }$ inductor, what is the emf across the inductor?