Question 1

A capacitor with initial charge $$Q_0 is $$connected in series with a resistor $$R as $$shown in the first image. The switch is initially open. What happens to the charge on the capacitor immediately after the switch is closed?

Accepted Answer

The charge on the capacitor remains at $$Q_0$$ and then decreases exponentially over time.

Question 2

Which equation correctly describes the charge $$q(t) on a $$discharging capacitor in an RC circuit?

Accepted Answer

$$q(t) = Q_0$ e$$^{-t/RC}$$

Question 3

In an RC circuit, what is the physical meaning of the time constant $$	au = RC$$?

Accepted Answer

It is the time required for the charge to decrease to $$1/e of $$its initial value during discharge.

Question 4

A capacitor is being charged in an RC circuit with a battery of emf $$\mathcal{E}. $$What is the final charge $$Q_f on $$the capacitor after a long time?

Accepted Answer

$$Q_f = C\mathcal{E}$$

Question 5

Which of the following best describes the current $$i(t) in a $$discharging RC circuit?

Accepted Answer

$$i(t) = \frac{Q_0$}{RC} e$$^{-t/RC}$$

Question 6

If the resistance $$R in an RC $$circuit is doubled, what happens to the time constant $$	au$$?

Accepted Answer

It doubles.

Question 7

A student claims that the current in an RC charging circuit increases over time. Is this correct?

Accepted Answer

No, the current decreases exponentially as the capacitor charges.

Question 8

Which of the following equations gives the current $$i(t) in an RC $$charging circuit immediately after the switch is closed?

Accepted Answer

$$i(0) = \frac{\mathcal{E}}{R}$$

Question 9

A fully charged capacitor is connected across a resistor. After a time $$t = RC$$, what fraction of the initial charge remains on the capacitor?

Accepted Answer

$$1/e$$

Question 10

Which of the following statements about the exponential decay of current in a discharging RC circuit is correct?

Accepted Answer

The current decreases exponentially and never truly reaches zero.

Question 11

A real battery has an internal resistance $$R_{int}. $$Which equation gives the terminal voltage $$V_{ab}$$ when a current $$i$$ flows?

Accepted Answer

$$V_{ab} = \mathcal{E} - iR_{int}$$

Question 12

Which of the following is a property of all magnets?

Accepted Answer

They always have both a north and a south pole.

Question 13

Which law states that the total magnetic flux through any closed surface is zero?

Accepted Answer

Gauss's law for magnetism

Question 14

What is the direction of the magnetic field around a straight current-carrying wire?

Accepted Answer

In circles centered on the wire, direction given by the right-hand rule

Question 15

Which equation gives the magnitude of the magnetic field $$B at a $$distance $$R$$ from a long, straight wire carrying current $$i$$?

Accepted Answer

$$B = \frac{\mu_0$ i}{2\pi R}$$

Question 16

A moving charge $$q$$ with velocity $$\vec{v}$$ enters a region with a uniform magnetic field $$\vec{B}. $$What is the magnitude of the magnetic force on the charge?

Accepted Answer

$$F = qvB \sin	heta$$

Question 17

Which of the following best describes the direction of the magnetic force on a positive charge moving in a magnetic field?

Accepted Answer

It is perpendicular to both the velocity and the magnetic field.

Question 18

If a bar magnet is cut in half, what happens to the magnetic poles?

Accepted Answer

Each piece has both a north and a south pole.

Question 19

Which of the following is true about the Earth's magnetic field?

Accepted Answer

The Earth's geographic north pole is actually a magnetic south pole.

RC Circuits: Charging and Discharging Capacitors

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