Question 1

Immediately after switch S in the circuit shown is closed, the current through the battery is: A)0 B)V₀/R₁ C)V₀/R₂ D)V₀/(R₁ + R₂) E)V₀(R₁ + R₂)/(R₁R₂)

Accepted Answer

The answer of Immediately after switch S in the circuit...

Question 2

The diagram shows an inductor that is part of a circuit.The direction of the emf induced in the inductor is indicated.Which of the following is possible? 
A)The current is constant and rightward
B)The current is constant and leftward
C)The current is increasing and rightward
D)The current is increasing and leftward
E)None of the above

Accepted Answer

According to Lenz's Law, the direction of the induced emf in an inductor opposes the change in current through it. Therefore, as the current through the inductor is increasing (as indicated by the arrow), the induced emf will be in the opposite direction (leftward). This means that the current must be increasing and leftward to produce the induced emf shown in the diagram. Therefore, choice D is the best answer.

Question 3

An inductance L, resistance R, and ideal battery of emf are wired in series and the circuit is allowed to come to equilibrium.A switch in the circuit is opened at time t = 0, at which time the current is /R.At any later time t the potential difference across the resistor is given by: A) (1 - e^-Lt^/^R) B) e^-^Lt^/^R C) (1 + e^-Rt^/^L) D) e^-Rt^/^L E) (1 - e^-Rt^/^L)

Accepted Answer

The answer of An inductance L, resistance R, and ideal...

Question 4

An inductor with inductance L and a resistor with resistance R are wired in series to an ideal battery with emf  .A switch in the circuit is closed at time t = 0, at which time the current is zero.A long time after the switch is thrown the potential differences across the inductor and resistor are:
A)0, 
B)  , 0
C)  /2,
 /2
D)(L/R)  , (R/L)

E)unknown since the rate of change of the current is not given

Accepted Answer

The answer of An inductor with inductance L and a...

Question 5

When the switch S in the circuit shown is closed, the time constant for the growth of current in R₂ is: A)L/R₁ B)L/R₂ C)L/(R₁ + R₂) D)L(R₁ + R₂)/(R₁R₂) E)(L/R₁ + L/R₂)/2

Accepted Answer

The time constant for a circuit with a resistor and an inductor is given by τ = L/R where L is the inductance and R is the resistance. In this circuit, the current will flow through R₂ and the inductor L when the switch S is closed. Therefore, the time constant for the growth of current in R₂ is τ = L/R₂.

Question 6

A 3.5 mH inductor and a 4.5 mH inductor are connected in parallel.When the total emf of the combination is 16 V, the rate of change of the current in the larger inductor is: A)2.0 * 10³ A/s B)3.6 * 10³ A/s C)4.6*10³ A/s D)7.0 * 10³ A/s E)8.1 *10³ A/s

Accepted Answer

The rate of change of current in an inductor is given by $V = L \frac{dI}{dt}$, where $V$ is the voltage across the inductor, $L$ is the inductance, and $\frac{dI}{dt}$ is the rate of change of current. For the larger inductor (4.5 mH), rearranging the formula gives $\frac{dI}{dt} = \frac{V}{L} = \frac{16}{4.5 \times 10^{-3}} = 3.56 \times 10^{3} A/s$, which is approximately $3.6 \times 10^{3} A/s$.

Question 7

An inductance L and a resistance R are connected in series to an ideal battery.A switch in the circuit is closed at time t = 0, at which time the current is zero.The rate of increase of the energy stored in the inductor is a maximum:
A)just after the switch is closed
B)at the time t = L/R after the switch is closed
C)at the time t = 2L/R after the switch is closed
D)at the time t = (L/R)ln 2 after the switch is closed
E)a long time after the switch is closed

Accepted Answer

The rate of increase of energy stored in the inductor is maximum when the current through the inductor is increasing most rapidly, which occurs at the time $t = \frac{L}{R}\ln 2$, according to the time constant of an RL circuit.

Question 8

An inductance L, resistance R, and ideal battery of emf are wired in series and the circuit is allowed to come to equilibrium.A switch in the circuit is opened at time t = 0, at which time the current is /R.At any later time t the current i is given by: A)( /R)(1 - e^-Lt^/^R) B)( /R)e^-^Lt^/^R C)( /R)(1 + e^-^Rt^/^L) D)( /R)e^-^Rt^/^L E)( /R)(1 - e^-^Rt^/^L)

Accepted Answer

The answer of An inductance L, resistance R, and ideal...

Question 9

If both the resistance and the inductance in an LR series circuit are doubled the new inductive time constant will be:
A)twice the old
B)four times the old
C)half the old
D)one-fourth the old
E)unchanged

Accepted Answer

The inductive time constant for an LR circuit is given by τ = L/R, where L is the inductance and R is the resistance. If both L and R are doubled, the ratio L/R remains unchanged, meaning the inductive time constant remains the same.

Question 10

A 3.5 mH inductor and a 4.5 mH inductor are connected in series and a time varying current is established in them.When the total emf of the combination is 16 V, the emf of the larger inductor is:
A)2.3 V
B)7.0 V
C)9.0 V
D)28 V
E)36 V

Accepted Answer

The emf induced in an inductor is directly proportional to its inductance. When connected in series, the total inductance is the sum of individual inductances, which is 3.5 mH + 4.5 mH = 8.0 mH. The ratio of the larger inductor's inductance to the total inductance is 4.5 mH / 8.0 mH = 0.5625. Therefore, the emf across the larger inductor is 0.5625 * 16 V = 9.0 V.

Question 11

An inductance L, resistance R, and ideal battery of emf are wired in series.A switch in the circuit is closed at time t = 0, at which time the current is zero.At any later time t the emf of the inductor is given by: A) (1 - e^-^Lt^/^R) B) e^-^Lt^/^R C) (1 + e^-^Rt^/^L) D) e^-^Rt^/^L E) (1 - e^-^Rt^/^L)

Accepted Answer

The answer of An inductance L, resistance R, and ideal...

Question 12

An 8.0-mH inductor and a 2.0-$\Omega$resistor are wired in series to an ideal battery.A switch in the circuit is closed at time t = 0, at which time the current is zero.The current reaches half its final value at a time of:
A)2.8 ms
B)4.0 ms
C)3.0 s
D)170 s
E)250 s

Accepted Answer

The time constant for an LR circuit is given by $\tau = \frac{L}{R}$, where $L$ is the inductance and $R$ is the resistance. Here, $L = 8.0 \, \text{mH} = 8.0 \times 10^{-3} \, \text{H}$ and $R = 2.0 \, \Omega$, so $\tau = \frac{8.0 \times 10^{-3}}{2.0} = 4.0 \times 10^{-3} \, \text{s} = 4.0 \, \text{ms}$. The current in an LR circuit reaches (1 - 1/e) of its final value after one time constant, which is approximately 63%. To reach half (50%) of its final value, it would take less time than one time constant. Therefore, the only option less than 4.0 ms is 2.8 ms.

Question 13

A 3.5 mH inductor and a 4.5 mH inductor are connected in parallel.The equivalent inductance is:
A)0.13 mH
B)0.51 mH
C)1.0 mH
D)2.0 mH
E)8.0 mH

Accepted Answer

The answer of A 3.5 mH inductor and a 4.5...

Question 14

An inductor with inductance L and an inductor with inductance 2L are connected in parallel.When the rate of change of the current in the larger inductor is 2000 A/s the rate of change of the current in the smaller is:
A)400 A/s
B)1000 A/s
C)1600 A/s
D)2000 A/s
E)4000 A/s

Accepted Answer

In parallel, the voltage across inductors is the same. Using V = L(di/dt), for the larger inductor: V = 2L(2000 A/s). For the smaller inductor: V = L(di/dt). Equating the two: L(di/dt) = 2L(2000 A/s), so di/dt = 4000 A/s.

Question 15

The diagrams show three circuits with identical batteries, identical inductors, and identical resistors.Rank them according to the current through the battery just after the switch is closed, from least to greatest. 
A)3, 2, 1
B)2 and 3 tie, then 1
C)1, 3, 2
D)1, 2, 3
E)2, 3, 1

Accepted Answer

In circuit 1, the inductor has no effect as it is shorted by the switch, so the initial current through the battery is simply determined by the resistance of the circuit. In circuit 2, as the switch is closed, the inductor opposes changes in current, and initially behaves as if it were a resistor. This means that the total resistance of the circuit, and therefore the initial current, is greater than in circuit 1. In circuit 3, the inductor initially behaves like a short circuit, effectively bypassing the resistor, so the total resistance of the circuit and therefore the initial current is the lowest of the three.

Question 16

An 8.0-mH inductor and a 2.0- $\Omega$ resistor are wired in series to a 20-V ideal battery.A switch in the circuit is closed at time t = 0, at which time the current is zero.After a long time the current in the resistor and the current in the inductor are:
A)0 A, 0 A
B)10 A, 10 A
C)2.5 A, 2.5 A
D)10 A, 2.5 A
E)10 A, 0 A

Accepted Answer

After a long time, the inductor acts like a short circuit (its reactance becomes zero), so the current in the circuit is determined only by the resistor. Using Ohm's Law (V = IR), the current I = V/R = 20V/2Ω = 10 A. This current flows through both the resistor and the inductor.

Question 17

A 6.0 mH inductor is in a circuit.At the instant the current is 5.0 A and its rate of change is 200 A/s, the rate with which the energy stored in the inductor is increasing is: A)7.5*10^-2 W B)3.0 W C)6.0 W D)120 W E)240 W

Accepted Answer

The answer of A 6.0 mH inductor is in a...

Question 18

An inductance L, resistance R, and ideal battery of emf are wired in series.A switch in the circuit is closed at time t = 0, at which time the current is zero.At any later time t the current i is given by: A)( /R)(1 - e^-Lt^/^R) B)( /R)e^-^Lt^/^R C)( /R)(1 + e^-^Rt^/^L) D)( /R)e^-^Rt^/^L E)( /R)(1 - e^-^Rt^/^L)

Accepted Answer

The answer of An inductance L, resistance R, and ideal...

Question 19

An inductance L, resistance R, and ideal battery of emf are wired in series.A switch in the circuit is closed at time t = 0, at which time the current is zero.At any later time t the potential difference across the resistor is given by: A) (1 - e^-Lt^/^R) B) e^-^Lt^/^R C) (1 + e^-Rt^/^L) D) e^-Rt^/^L E) (1 - e^-Rt^/^L)

Accepted Answer

The answer of An inductance L, resistance R, and ideal...

Question 20

An 8.0-mH inductor and a 2.0- $\Omega$ resistor are wired in series to a 20-V ideal battery.A switch in the circuit is closed at time t = 0, at which time the current is zero.Immediately after the switch is thrown the potential differences across the inductor and resistor are:
A)0 V, 20 V
B)20 V, 0 V
C)10 V, 10 V
D)16 V, 4 V
E)unknown since the rate of change of the current is not given

Accepted Answer

Immediately after the switch is thrown, there is no current flowing in the circuit. Therefore, there is no voltage drop across the resistor (Ohm's Law: V = IR), and the entire voltage of the battery (20 V) is applied across the inductor. Therefore, the potential differences across the inductor and resistor are 20 V and 0 V, respectively, making choice B the correct answer.

Quiz 30: Induction and Inductance

Immediately after switch S in the circuit shown is closed, the current through the battery is:

The diagram shows an inductor that is part of a circuit.The direction of the emf induced in the inductor is indicated.Which of the following is possible?

An inductance L, resistance R, and ideal battery of emf are wired in series and the circuit is allowed to come to equilibrium.A switch in the circuit is opened at time t = 0, at which time the current is /R.At any later time t the potential difference across the resistor is given by:

An inductor with inductance L and a resistor with resistance R are wired in series to an ideal battery with emf .A switch in the circuit is closed at time t = 0, at which time the current is zero.A long time after the switch is thrown the potential differences across the inductor and resistor are:

When the switch S in the circuit shown is closed, the time constant for the growth of current in R₂ is:

A 3.5 mH inductor and a 4.5 mH inductor are connected in parallel.When the total emf of the combination is 16 V, the rate of change of the current in the larger inductor is:

An inductance L and a resistance R are connected in series to an ideal battery.A switch in the circuit is closed at time t = 0, at which time the current is zero.The rate of increase of the energy stored in the inductor is a maximum:

An inductance L, resistance R, and ideal battery of emf are wired in series and the circuit is allowed to come to equilibrium.A switch in the circuit is opened at time t = 0, at which time the current is /R.At any later time t the current i is given by:

If both the resistance and the inductance in an LR series circuit are doubled the new inductive time constant will be:

A 3.5 mH inductor and a 4.5 mH inductor are connected in series and a time varying current is established in them.When the total emf of the combination is 16 V, the emf of the larger inductor is:

An inductance L, resistance R, and ideal battery of emf are wired in series.A switch in the circuit is closed at time t = 0, at which time the current is zero.At any later time t the emf of the inductor is given by:

An 8.0-mH inductor and a 2.0- $\Omega$ resistor are wired in series to an ideal battery.A switch in the circuit is closed at time t = 0, at which time the current is zero.The current reaches half its final value at a time of:

A 3.5 mH inductor and a 4.5 mH inductor are connected in parallel.The equivalent inductance is:

An inductor with inductance L and an inductor with inductance 2L are connected in parallel.When the rate of change of the current in the larger inductor is 2000 A/s the rate of change of the current in the smaller is:

The diagrams show three circuits with identical batteries, identical inductors, and identical resistors.Rank them according to the current through the battery just after the switch is closed, from least to greatest.

An 8.0-mH inductor and a 2.0- $\Omega$ resistor are wired in series to a 20-V ideal battery.A switch in the circuit is closed at time t = 0, at which time the current is zero.After a long time the current in the resistor and the current in the inductor are:

A 6.0 mH inductor is in a circuit.At the instant the current is 5.0 A and its rate of change is 200 A/s, the rate with which the energy stored in the inductor is increasing is:

An inductance L, resistance R, and ideal battery of emf are wired in series.A switch in the circuit is closed at time t = 0, at which time the current is zero.At any later time t the current i is given by:

An inductance L, resistance R, and ideal battery of emf are wired in series.A switch in the circuit is closed at time t = 0, at which time the current is zero.At any later time t the potential difference across the resistor is given by:

An 8.0-mH inductor and a 2.0- $\Omega$ resistor are wired in series to a 20-V ideal battery.A switch in the circuit is closed at time t = 0, at which time the current is zero.Immediately after the switch is thrown the potential differences across the inductor and resistor are:

Quiz 30: Induction and Inductance

Immediately after switch S in the circuit shown is closed, the current through the battery is:

The diagram shows an inductor that is part of a circuit.The direction of the emf induced in the inductor is indicated.Which of the following is possible?

An inductance L, resistance R, and ideal battery of emf are wired in series and the circuit is allowed to come to equilibrium.A switch in the circuit is opened at time t = 0, at which time the current is /R.At any later time t the potential difference across the resistor is given by:

An inductor with inductance L and a resistor with resistance R are wired in series to an ideal battery with emf .A switch in the circuit is closed at time t = 0, at which time the current is zero.A long time after the switch is thrown the potential differences across the inductor and resistor are:

When the switch S in the circuit shown is closed, the time constant for the growth of current in R2 is:

A 3.5 mH inductor and a 4.5 mH inductor are connected in parallel.When the total emf of the combination is 16 V, the rate of change of the current in the larger inductor is:

An inductance L and a resistance R are connected in series to an ideal battery.A switch in the circuit is closed at time t = 0, at which time the current is zero.The rate of increase of the energy stored in the inductor is a maximum:

An inductance L, resistance R, and ideal battery of emf are wired in series and the circuit is allowed to come to equilibrium.A switch in the circuit is opened at time t = 0, at which time the current is /R.At any later time t the current i is given by:

If both the resistance and the inductance in an LR series circuit are doubled the new inductive time constant will be:

A 3.5 mH inductor and a 4.5 mH inductor are connected in series and a time varying current is established in them.When the total emf of the combination is 16 V, the emf of the larger inductor is:

An inductance L, resistance R, and ideal battery of emf are wired in series.A switch in the circuit is closed at time t = 0, at which time the current is zero.At any later time t the emf of the inductor is given by:

An 8.0-mH inductor and a 2.0- Ω\OmegaΩ resistor are wired in series to an ideal battery.A switch in the circuit is closed at time t = 0, at which time the current is zero.The current reaches half its final value at a time of:

A 3.5 mH inductor and a 4.5 mH inductor are connected in parallel.The equivalent inductance is:

An inductor with inductance L and an inductor with inductance 2L are connected in parallel.When the rate of change of the current in the larger inductor is 2000 A/s the rate of change of the current in the smaller is:

The diagrams show three circuits with identical batteries, identical inductors, and identical resistors.Rank them according to the current through the battery just after the switch is closed, from least to greatest.

An 8.0-mH inductor and a 2.0- Ω\OmegaΩ resistor are wired in series to a 20-V ideal battery.A switch in the circuit is closed at time t = 0, at which time the current is zero.After a long time the current in the resistor and the current in the inductor are:

A 6.0 mH inductor is in a circuit.At the instant the current is 5.0 A and its rate of change is 200 A/s, the rate with which the energy stored in the inductor is increasing is:

An inductance L, resistance R, and ideal battery of emf are wired in series.A switch in the circuit is closed at time t = 0, at which time the current is zero.At any later time t the current i is given by:

An inductance L, resistance R, and ideal battery of emf are wired in series.A switch in the circuit is closed at time t = 0, at which time the current is zero.At any later time t the potential difference across the resistor is given by:

An 8.0-mH inductor and a 2.0- Ω\OmegaΩ resistor are wired in series to a 20-V ideal battery.A switch in the circuit is closed at time t = 0, at which time the current is zero.Immediately after the switch is thrown the potential differences across the inductor and resistor are:

When the switch S in the circuit shown is closed, the time constant for the growth of current in R₂ is:

An 8.0-mH inductor and a 2.0- $\Omega$ resistor are wired in series to an ideal battery.A switch in the circuit is closed at time t = 0, at which time the current is zero.The current reaches half its final value at a time of:

An 8.0-mH inductor and a 2.0- $\Omega$ resistor are wired in series to a 20-V ideal battery.A switch in the circuit is closed at time t = 0, at which time the current is zero.After a long time the current in the resistor and the current in the inductor are:

An 8.0-mH inductor and a 2.0- $\Omega$ resistor are wired in series to a 20-V ideal battery.A switch in the circuit is closed at time t = 0, at which time the current is zero.Immediately after the switch is thrown the potential differences across the inductor and resistor are: