Q: Which physical quantity determines the rate at which the bulb dims after the switch is closed?

The time constant $$\tau = RC$$

Question 1

Which law is most directly used to analyze the loop in the circuit shown, containing the resistor $$R$$, capacitor $$C$$, and bulb, after the switch $$S is $$closed?

Accepted Answer

Kirchhoff's Voltage Law (KVL)

Question 2

Immediately after the switch $$S is $$closed in the circuit, what is the initial current through the bulb?

Accepted Answer

$$I_0$$ = \frac{V}{R}$$, because the uncharged capacitor acts as a short circuit.

Question 3

As time progresses after the switch $$S is $$closed, what happens to the brightness of the bulb?

Accepted Answer

It decreases as the current through the bulb decreases.

Question 4

Which equation describes the current $$I(t)$$ through the bulb as a function of time after the switch is closed?

Accepted Answer

$$I(t) = \frac{V}{R} e$$^{-t/RC}$$

Question 5

What is the final voltage across the capacitor $$C$$ after a long time?

Accepted Answer

$$V_C = V$$

Question 6

If the resistance $$R is $$doubled, how does the time constant $$	au of $$the circuit change?

Accepted Answer

$$	au is $$doubled

Question 7

Suppose the bulb is replaced with a second resistor of resistance $$R. $$What is the total resistance in the circuit?

Accepted Answer

$$R_{total} = 2R$$

Question 8

If the battery is removed after the capacitor is fully charged, what happens to the bulb?

Accepted Answer

It flashes briefly as the capacitor discharges.

Question 9

Which physical quantity determines the rate at which the bulb dims after the switch is closed?

Accepted Answer

The time constant $$	au = RC$$

Question 10

If the circuit is modified so that the capacitor is initially charged to voltage $$V$$ and then the switch is closed, what is the initial current through the bulb?

Accepted Answer

$$I_0$$ = \frac{V}{R}$$

Question 11

Which of the following best describes the energy transformation in the circuit after the switch is closed?

Accepted Answer

Electrical energy is converted to light and heat in the bulb, and stored as electric potential energy in the capacitor.

Question 12

If the capacitance $$C is $$increased, what happens to the time it takes for the bulb to dim?

Accepted Answer

It increases.

Question 13

What is the expression for the charge $$Q(t) on $$the capacitor as a function of time after the switch is closed?

Accepted Answer

$$Q(t) = CV (1 - e$$^{-t/RC}$$)$$

Question 14

If the bulb is rated for a maximum current $$I_{max}$$, what is the maximum safe voltage $$V_{max}$$ for the battery?

Accepted Answer

$$V_{max} = I_{max} R$$

Question 15

Which of the following statements is true about the circuit when the capacitor is fully charged?

Accepted Answer

The current through the bulb is zero.

Physics with Calculus Quiz Study Guide: Circuits, Capacitors, and Electric Potential

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