Q: A 1.0 mH inductor is used in an LC circuit that must oscillate at 920 kHz. What is the required capacitance?

$$C = \frac{1}{(2\pi \times 920 \times 10^3$)^2$$ \times 1.0 \times $$10^{-3}$$}$

Question 1

In an LC circuit, what is the physical analogy for the maximum charge on the capacitor?

Accepted Answer

A fully compressed spring at rest

Question 2

What is the expression for the angular frequency $$\omega of $$oscillation in an LC circuit?

Accepted Answer

$$\omega = \frac{1}{\sqrt{LC}}$$

Question 3

A 1.0 mH inductor is used in an LC circuit that must oscillate at 920 kHz. What is the required capacitance?

Accepted Answer

$$C = \frac{1}{(2\pi 	imes 920 	imes 10^3$)^2$$ 	imes 1.0 	imes $$10^{-3}$$}$

Question 4

In an LC circuit, what happens to the current when the capacitor is fully discharged?

Accepted Answer

The current is at its maximum

Question 5

Which of the following best describes the energy transformation in an ideal LC circuit?

Accepted Answer

Energy oscillates between the electric field of the capacitor and the magnetic field of the inductor

Question 6

For an LR circuit, what is the time constant $$	au$$?

Accepted Answer

$$	au = \frac{L}{R}$$

Question 7

Immediately after closing the switch in an LR circuit, what is the current through the inductor?

Accepted Answer

It is zero

Question 8

After a long time, what is the current through the inductor in an LR circuit with a battery of voltage $$V$$ and resistance $$R$$?

Accepted Answer

$$I = \frac{V}{R}$$

Question 9

Which law states that the direction of induced current opposes the change in magnetic flux?

Accepted Answer

Lenz's Law

Question 10

What is the mathematical expression for the induced emf in a coil of $$N$$ turns according to Faraday's Law?

Accepted Answer

$$\varepsilon = -N \frac{d\Phi_B}{dt}$$

Question 11

A loop of area $$A is $$placed in a uniform magnetic field $$B at an $$angle $$	heta. $$What is the magnetic flux through the loop?

Accepted Answer

$$\Phi_B = AB\cos	heta$$

Question 12

Which of the following will NOT change the magnetic flux through a loop?

Accepted Answer

Moving the loop parallel to the magnetic field lines

Question 13

A cell phone uses an LC circuit to establish its transmission frequency. If the inductance is doubled and the capacitance is halved, what happens to the oscillation frequency?

Accepted Answer

It decreases by a factor of $$\sqrt{2}$$

Question 14

What is the energy stored in an inductor with inductance $$L$$ carrying current $$I$$?

Accepted Answer

$$U_L = \frac{1}{2}LI^2$

Question 15

Which of the following is a correct expression for the motional emf generated when a conductor of length $$l$$ moves at velocity $$v$$ perpendicular to a magnetic field $$B$$?

Accepted Answer

$$\varepsilon = vBl$$

Question 16

If the current in an LR circuit has decreased to 13% of its initial value, how much time has passed?

Accepted Answer

$$t = 2	au$$

Question 17

Which of the following best describes the current in an ideal LC circuit over time?

Accepted Answer

It oscillates sinusoidally

Question 18

A solenoid has $$N$$ turns, length $$l$$, and cross-sectional area $$A. $$What is its inductance?

Accepted Answer

$$L = \mu_0$ N^2$ A / l$$

Question 19

Which of the following is NOT a way to induce an emf in a loop?

Accepted Answer

Keeping the loop stationary in a constant magnetic field

Question 20

In an LR circuit, what is the potential difference across the inductor as the current changes?

Accepted Answer

$$\Delta V_L = -L \frac{dI}{dt}$$

Study Notes: LC and LR Circuits, Electromagnetic Induction, and Applications

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