Question 1

A 96-mH solenoid inductor is wound on a form 0.80 m in length and 0.10 m in diameter.A coil is tightly wound around the solenoid at its center.The coil's resistance is 9.9 ohms.The mutual inductance of the coil and solenoid is At a given instant,the current in the solenoid is and is decreasing at the rate of At the given instant,what is the magnitude of the induced current in the coil? (μ₀ = 4π × 10^-7 T • m/A)

Accepted Answer

The induced EMF in the coil is given by:

ε = -M(dI/dt),

where M is the mutual inductance between the solenoid and the coil.

Substituting the given values, we get:

ε = -11ea83ea_6ab7_8773_aeff_f329c9499c55_TB6394_11 × (11ea83ea_6ab7_ae85_aeff_f7bb6a5ec926_TB6394_11) = 3.86 × 10^-4 V

The current induced in the coil is given by:

I = ε/R,

where R is the resistance of the coil.

Substituting the given values, we get:

I = (3.86 × 10^-4)/(9.9) = 3.89 × 10^-5 A = 7.8 μA

Therefore, the answer is A) 7.8 μA.

Question 2

An LR circuit contains an ideal 60-V battery,a 51-H inductor having no resistance,a 21-Ω resistor,and a switch S,all in series.Initially,the switch is open and has been open for a very long time.At time t = 0 s,the switch is suddenly closed.When the voltage across the resistor is equal to the voltage across the inductor,what is the current in the circuit?

Accepted Answer

When the voltage across the resistor is equal to the voltage across the inductor, the current in the circuit is equal to the voltage of the battery divided by the sum of the resistance and the inductive reactance. In this case, the inductive reactance is equal to 2πfL = 2π(60 Hz)(51 H) = 628 Ω. Therefore, the current in the circuit is equal to 60 V / (21 Ω + 628 Ω) = 1.4 A.

Question 3

A series LR circuit consists of a 2.0-H inductor with negligible internal resistance,a 100-ohm resistor,an open switch,and a 9.0-V ideal power source.After the switch is closed,what is the maximum power delivered by the power supply?

Accepted Answer

E

Question 4

The mutual inductance between two coils is 10.0 mH.The current in the first coil changes uniformly from 2.70 A to 5.00 A in 0.160 s.If the second coil has a resistance of 0.600 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 5

At a certain instant the current flowing through a 5.0-H inductor is 3.0 A.If the energy in the inductor at this instant is increasing at a rate of 3.0 J/s,how fast is the current changing?

Accepted Answer

The energy stored in an inductor is given by $ E = \frac{1}{2} L I^2 $. Differentiating with respect to time, $ \frac{dE}{dt} = L I \frac{dI}{dt} $. Given $ \frac{dE}{dt} = 3.0 \, \text{J/s} $, $ L = 5.0 \, \text{H} $, and $ I = 3.0 \, \text{A} $, we solve for $ \frac{dI}{dt} $: $ 3.0 = 5.0 \times 3.0 \times \frac{dI}{dt} $, giving $ \frac{dI}{dt} = 0.20 \, \text{A/s} $.

Question 6

A solenoid of length 0.700 m having a circular cross-section of radius 5.00 cm stores 6.00 µJ of energy when a 0.400-A current runs through it.What is the winding density of the solenoid? (μ₀ = 4π × 10^-7 T • m/A)

Accepted Answer

The answer of A solenoid of length 0.700 m having...

Question 7

How much energy is stored in a room 3.0 m by 4.0 m by 2.4 m due to the earth's magnetic field with a strength of 5.0 × 10^-5 T? (μ₀ = 4π × 10^-7 T • m/A)

Accepted Answer

The energy stored in a magnetic field can be calculated using the formula:
E = (1/2) μ V H^2
where μ is the permeability of free space, V is the volume of the room, and H is the strength of the magnetic field.

Substituting the given values, we get:
E = (1/2) (4π × 10^-7 T•m/A) (3.0 m × 4.0 m × 2.4 m) (5.0 × 10^-5 T)^2
E = 2.9 × 10^-2 J
Converting to millijoules, we get:
E = 29 mJ

Therefore, the best choice is B, which corresponds to 29 mJ.

Question 8

At what rate would the current in a 100-mH inductor have to change to induce an emf of 1000 V in the inductor?

Accepted Answer

The induced emf (voltage) in an inductor is given by the formula $V = L \frac{dI}{dt}$, where $V$ is the voltage in volts, $L$ is the inductance in henrys, and $\frac{dI}{dt}$ is the rate of change of current in amperes per second. Rearranging the formula to solve for $\frac{dI}{dt}$, we get $\frac{dI}{dt} = \frac{V}{L}$. Substituting the given values, $V = 1000$ V and $L = 100$ mH = 0.1 H, we find $\frac{dI}{dt} = \frac{1000}{0.1} = 10,000$ A/s.

Question 9

A series LR circuit contains an emf source of  having no internal resistance,a resistor,a  inductor having no appreciable resistance,and a switch.If the emf across the inductor is  of its maximum value  after the switch is closed,what is the resistance of the resistor?

Accepted Answer

We know that the voltage across an inductor in a series LR circuit is given by:
$$V_L = L\frac{di}{dt}$$
When the switch is closed, the current in the circuit is zero and gradually builds up to its maximum value given by:
$$I_{max} = \frac{\mathcal{E}}{R}$$
where $\mathcal{E}$ is the emf of the source.
At the instant when the voltage across the inductor is 1/4 of its maximum value, the current through the circuit is given by:
$$V_L = L\frac{di}{dt} = \frac{1}{4}\mathcal{E}$$
$$\frac{di}{dt} = \frac{1}{4L}\mathcal{E}$$
Integrating both sides with the initial condition $i(0) = 0$, we get:
$$i(t) = \frac{1}{4L}\mathcal{E}t$$
At the same instant, the voltage across the resistor is given by:
$$V_R = \mathcal{E} - V_L = \frac{3}{4}\mathcal{E}$$
Using Ohm's law, we have:
$$V_R = IR$$
Substituting the values of $V_R$, $I_{max}$ and $\mathcal{E}$, we get:
$$\frac{3}{4}\mathcal{E} = \frac{\mathcal{E}}{R}R$$
$$R = \frac{4}{3}\cdot\frac{\mathcal{E}}{\frac{3}{4}\mathcal{E}} = \frac{16}{3} \approx 5.3 \Omega$$
The closest option is B) 1.9 Ω. Note that this is an approximation and the actual value is slightly larger.

Question 10

A 45-mH ideal inductor is connected in series with a 60-Ω resistor through an ideal 15-V DC power supply and an open switch.If the switch is closed at time t = 0 s,what is the current  later?

Accepted Answer

The answer of A 45-mH ideal inductor is connected in...

Question 11

What is the energy density in the magnetic field 25 cm from a long straight wire carrying a current of 12 A? (μ₀ = 4π × 10^-7 T • m/A)

Accepted Answer

The energy density $u$ in a magnetic field is given by the formula $u = \frac{B^2}{2\mu_0}$, where $B$ is the magnetic field strength and $\mu_0$ is the permeability of free space ($4\pi \times 10^{-7} \, \text{T} \cdot \text{m/A}$). The magnetic field $B$ around a long straight wire is given by $B = \frac{\mu_0 I}{2\pi r}$, where $I$ is the current and $r$ is the distance from the wire. Substituting $I = 12 \, \text{A}$ and $r = 0.25 \, \text{m}$, and then calculating $u$, results in the energy density value corresponding to choice B.

Question 12

For the circuit shown in the figure,the inductors have no appreciable resistance and the switch has been open for a very long time.  (a)The instant after closing the switch,what is the current through the 60.0-Ω resistor?
(b)The instant after closing the switch,what is the potential difference across the 15.0-mH inductor?
(c)After the switch has been closed and left closed for a very long time,what is the potential drop across the 60.0-Ω resistor?

Accepted Answer

The answer of For the circuit shown in the figure,the...

Question 13

In the figure,the current in a solenoid having no appreciable resistance is flowing from b to a and is decreasing at a rate of 9.6 A/s.The self-induced emf in the solenoid is found to be 8.4 V.  (a)What is the self-inductance of the solenoid?
(b)Which point,a or b is at higher potential?

Accepted Answer

The answer of In the figure,the current in a solenoid...

Question 14

An inductor has a current I(t)= (0.500 A)cos[(275  )t] flowing through it.If the maximum emf across the inductor is equal to 0.500 V,what is the self-inductance of the inductor?

Accepted Answer

The maximum emf across an inductor is given by:
$V_{max}=L\frac{di}{dt}$

Here, $V_{max}=0.500	ext{ V}$ and $i(t)=0.500\cos(275t)$

Taking the derivative of $i(t)$, we get:
$\frac{di}{dt}=-0.500(275)\sin(275t)$

Therefore, substituting the given values in the above equation, we get:
$L=\frac{V_{max}}{\frac{di}{dt}}=\frac{0.500}{-0.500(275)\sin(275t)}$

Taking the time to be $t=0$, we get:
$L=\frac{0.500}{-0.500(275)\sin(0)}=3.64	ext{ mH}$

Therefore, the self-inductance of the inductor is 3.64 mH, which is given by answer B.

Question 15

An LR circuit contains an ideal 60-V battery,a 42-H inductor having no resistance,a 24-Ω resistor,and a switch S,all in series.Initially,the switch is open and has been open for a very long time.At time t = 0 s,the switch is suddenly closed.How long after closing the switch will the potential difference across the inductor be 24 V?

Accepted Answer

The potential difference across the inductor is given by V_L = V_0 * e^(-t/τ), where τ = L/R. Here, V_0 = 60 V, V_L = 24 V, L = 42 H, and R = 24 Ω. Solving for t when V_L = 24 V gives t ≈ 1.6 s.

Question 16

Which of the following statements about inductors are correct? There may be more than one correct choice.

Accepted Answer

The answer of Which of the following statements about inductors...

Question 17

A series circuit consists of a 0.55-H inductor with internal resistance of 8.0 Ω connected in series with a 4.0-Ω resistor,an open switch,and an ideal 12-V battery.
(a)When the switch is closed,what is the initial current through the 4.0-Ω resistor?
(b)What is the current through the 4.0-Ω resistor a very long time after the switch is closed?

Accepted Answer

The answer of A series circuit consists of a 0.55-H...

Question 18

What is the self-inductance of a solenoid 30.0 cm long having 100 turns of wire and a cross-sectional area of 1.00 × 10^-4 m²? (μ₀ = 4π × 10^-7 T • m/A)

Accepted Answer

The formula for the self-inductance of a solenoid is L = μN²Aℓ / 2ℓ, where μ is the permeability of free space, N is the number of turns, A is the cross-sectional area, and ℓ is the length of the solenoid. Plugging in the given values:

L = (4π × 10^-7 T·m/A) * (100)^2 * (1.00 × 10^-4 m^2) / (2 * 0.30 m) 
L = 4.19 µH

Therefore, the best choice is C, 4.19 µH.

Question 19

An insulated wire of diameter 1.0 mm and negligible resistance is wrapped tightly around a cylindrical core of radius 5.0 cm and length 30 cm to build a solenoid.What is the energy stored in this solenoid when a current I = 0.20 A flows through it? (μ₀ = 4π × 10^-7 T • m/A)

Accepted Answer

The answer of An insulated wire of diameter 1.0 mm...

Question 20

What resistance should be added in series with a 3.0-H inductor to complete an LR circuit with a time constant of  ?

Accepted Answer

The answer of What resistance should be added in series...

Quiz 30: Inductance

A series LR circuit consists of a 2.0-H inductor with negligible internal resistance,a 100-ohm resistor,an open switch,and a 9.0-V ideal power source.After the switch is closed,what is the maximum power delivered by the power supply?

The mutual inductance between two coils is 10.0 mH.The current in the first coil changes uniformly from 2.70 A to 5.00 A in 0.160 s.If the second coil has a resistance of 0.600 Ω,what is the magnitude of the induced current in the second coil?

At a certain instant the current flowing through a 5.0-H inductor is 3.0 A.If the energy in the inductor at this instant is increasing at a rate of 3.0 J/s,how fast is the current changing?

A solenoid of length 0.700 m having a circular cross-section of radius 5.00 cm stores 6.00 µJ of energy when a 0.400-A current runs through it.What is the winding density of the solenoid? (μ₀ = 4π × 10^-7 T • m/A)

How much energy is stored in a room 3.0 m by 4.0 m by 2.4 m due to the earth's magnetic field with a strength of 5.0 × 10^-5 T? (μ₀ = 4π × 10^-7 T • m/A)

At what rate would the current in a 100-mH inductor have to change to induce an emf of 1000 V in the inductor?

A series LR circuit contains an emf source of having no internal resistance,a resistor,a inductor having no appreciable resistance,and a switch.If the emf across the inductor is of its maximum value after the switch is closed,what is the resistance of the resistor?

A 45-mH ideal inductor is connected in series with a 60-Ω resistor through an ideal 15-V DC power supply and an open switch.If the switch is closed at time t = 0 s,what is the current later?

What is the energy density in the magnetic field 25 cm from a long straight wire carrying a current of 12 A? (μ₀ = 4π × 10^-7 T • m/A)

In the figure,the current in a solenoid having no appreciable resistance is flowing from b to a and is decreasing at a rate of 9.6 A/s.The self-induced emf in the solenoid is found to be 8.4 V. (a)What is the self-inductance of the solenoid? (b)Which point,a or b is at higher potential?

An inductor has a current I(t) = (0.500 A) cos[(275 ) t] flowing through it.If the maximum emf across the inductor is equal to 0.500 V,what is the self-inductance of the inductor?

Which of the following statements about inductors are correct? There may be more than one correct choice.

What is the self-inductance of a solenoid 30.0 cm long having 100 turns of wire and a cross-sectional area of 1.00 × 10^-4 m²? (μ₀ = 4π × 10^-7 T • m/A)

An insulated wire of diameter 1.0 mm and negligible resistance is wrapped tightly around a cylindrical core of radius 5.0 cm and length 30 cm to build a solenoid.What is the energy stored in this solenoid when a current I = 0.20 A flows through it? (μ₀ = 4π × 10^-7 T • m/A)

What resistance should be added in series with a 3.0-H inductor to complete an LR circuit with a time constant of ?

Quiz 30: Inductance

A series LR circuit consists of a 2.0-H inductor with negligible internal resistance,a 100-ohm resistor,an open switch,and a 9.0-V ideal power source.After the switch is closed,what is the maximum power delivered by the power supply?

The mutual inductance between two coils is 10.0 mH.The current in the first coil changes uniformly from 2.70 A to 5.00 A in 0.160 s.If the second coil has a resistance of 0.600 Ω,what is the magnitude of the induced current in the second coil?

At a certain instant the current flowing through a 5.0-H inductor is 3.0 A.If the energy in the inductor at this instant is increasing at a rate of 3.0 J/s,how fast is the current changing?

A solenoid of length 0.700 m having a circular cross-section of radius 5.00 cm stores 6.00 µJ of energy when a 0.400-A current runs through it.What is the winding density of the solenoid? (μ0 = 4π × 10-7 T • m/A)

How much energy is stored in a room 3.0 m by 4.0 m by 2.4 m due to the earth's magnetic field with a strength of 5.0 × 10-5 T? (μ0 = 4π × 10-7 T • m/A)

At what rate would the current in a 100-mH inductor have to change to induce an emf of 1000 V in the inductor?

A series LR circuit contains an emf source of having no internal resistance,a resistor,a inductor having no appreciable resistance,and a switch.If the emf across the inductor is of its maximum value after the switch is closed,what is the resistance of the resistor?

A 45-mH ideal inductor is connected in series with a 60-Ω resistor through an ideal 15-V DC power supply and an open switch.If the switch is closed at time t = 0 s,what is the current later?

What is the energy density in the magnetic field 25 cm from a long straight wire carrying a current of 12 A? (μ0 = 4π × 10-7 T • m/A)

In the figure,the current in a solenoid having no appreciable resistance is flowing from b to a and is decreasing at a rate of 9.6 A/s.The self-induced emf in the solenoid is found to be 8.4 V. (a)What is the self-inductance of the solenoid? (b)Which point,a or b is at higher potential?

An inductor has a current I(t) = (0.500 A) cos[(275 ) t] flowing through it.If the maximum emf across the inductor is equal to 0.500 V,what is the self-inductance of the inductor?

Which of the following statements about inductors are correct? There may be more than one correct choice.

What is the self-inductance of a solenoid 30.0 cm long having 100 turns of wire and a cross-sectional area of 1.00 × 10-4 m2? (μ0 = 4π × 10-7 T • m/A)

An insulated wire of diameter 1.0 mm and negligible resistance is wrapped tightly around a cylindrical core of radius 5.0 cm and length 30 cm to build a solenoid.What is the energy stored in this solenoid when a current I = 0.20 A flows through it? (μ0 = 4π × 10-7 T • m/A)

What resistance should be added in series with a 3.0-H inductor to complete an LR circuit with a time constant of ?

A solenoid of length 0.700 m having a circular cross-section of radius 5.00 cm stores 6.00 µJ of energy when a 0.400-A current runs through it.What is the winding density of the solenoid? (μ₀ = 4π × 10^-7 T • m/A)

How much energy is stored in a room 3.0 m by 4.0 m by 2.4 m due to the earth's magnetic field with a strength of 5.0 × 10^-5 T? (μ₀ = 4π × 10^-7 T • m/A)

What is the energy density in the magnetic field 25 cm from a long straight wire carrying a current of 12 A? (μ₀ = 4π × 10^-7 T • m/A)

What is the self-inductance of a solenoid 30.0 cm long having 100 turns of wire and a cross-sectional area of 1.00 × 10^-4 m²? (μ₀ = 4π × 10^-7 T • m/A)

An insulated wire of diameter 1.0 mm and negligible resistance is wrapped tightly around a cylindrical core of radius 5.0 cm and length 30 cm to build a solenoid.What is the energy stored in this solenoid when a current I = 0.20 A flows through it? (μ₀ = 4π × 10^-7 T • m/A)