Q: A battery with emf $$\mathcal{E}$$ and internal resistance $$r is $$connected to a load resistor $$R_{\text{load}}. $$What is the expression for the current in the circuit?

$$I = \dfrac{\mathcal{E}}{R_{\text{load}} + r}$$

Question 1

A 12 V car battery has an internal resistance of $$0.1\ \Omega$$ and is connected to a $$10\ \Omega$$ headlight. What is the terminal voltage across the battery when the headlight is on?

Accepted Answer

$$11.9\ 	ext{V}$$

Question 2

Which of the following statements about resistors in series is correct?

Accepted Answer

The current through each resistor is the same.

Question 3

Three resistors, $$R_1 = 10$$\ \Omega$$, R_2$ = 5\ \Omega$$, and $$R_3 = 10$$\ \Omega$$, are connected in series to a 50$$\ 	ext{V}$$ battery. What is the current in the circuit?

Accepted Answer

$$2\ 	ext{A}$$

Question 4

Which of the following actions will increase the current in a series circuit with a fixed battery voltage?

Accepted Answer

Increasing the battery voltage.

Question 5

For three resistors in parallel, $$R_1 = 2$$\ \Omega$$, R_2$ = 100\ \Omega$$, $$R_3 = 20$$\ \Omega$$, what is the equivalent resistance?

Accepted Answer

$$18.7\ \Omega$$

Question 6

A $$100\ 	ext{V}$$ power supply is connected to the parallel circuit in the previous question. What is the total current supplied by the battery?

Accepted Answer

$$5.3\ 	ext{A}$$

Question 7

Which of the following is a correct application of Kirchhoff’s junction rule?

Accepted Answer

The sum of the currents entering a junction equals the sum of the currents leaving.

Question 8

A battery with emf $$\mathcal{E}$$ and internal resistance $$r is $$connected to a load resistor $$R_{	ext{load}}. $$What is the expression for the current in the circuit?

Accepted Answer

$$I = \dfrac{\mathcal{E}}{R_{	ext{load}} + r}$$

Question 9

In a simple RC circuit, the time constant $$	au is $$defined as:

Accepted Answer

$$	au = RC$$

Question 10

A capacitor in an RC circuit is charged to $$60\% of $$its maximum voltage. If $$	au = 2.0\ 	ext{s}$$, how long has the capacitor been charging?

Accepted Answer

$$t = 1.83\ 	ext{s}$$

Question 11

Which of the following best describes the effect of a short circuit across a battery with internal resistance?

Accepted Answer

The current is limited only by the internal resistance, leading to a very large current.

Question 12

A $$12\ 	ext{V}$$ battery with $$r = 0.1\ \Omega is $$short-circuited. What is the power dissipated inside the battery?

Accepted Answer

$$P = 360\ 	ext{W}$$

Question 13

Which of the following is true for capacitors in series?

Accepted Answer

The total capacitance is less than the smallest individual capacitance.

Question 14

A voltmeter is used to measure the voltage across a resistor in a circuit. Which of the following statements is correct?

Accepted Answer

The voltmeter should be connected in parallel with the resistor.

Question 15

In a complex circuit, which rule allows you to write equations for the sum of potential differences around any closed loop?

Accepted Answer

Kirchhoff’s loop rule

Question 16

A refrigerator and a light bulb are connected in parallel to the same power source. If the refrigerator draws a large current, what happens to the brightness of the bulb if the wire resistance is significant?

Accepted Answer

The bulb dims due to a larger voltage drop across the wire resistance.

Question 17

Which of the following equations correctly describes the charging of a capacitor in an RC circuit?

Accepted Answer

$$V = \mathcal{E}\left(1 - \exp\left(-\dfrac{t}{RC}\right)\right)$$

Question 18

A $$0.04\ \Omega$$ flash lamp is discharged by a capacitor with a time constant of $$0.1\ \mu	ext{s}. $$What is the value of the capacitor?

Accepted Answer

$$2.5\ \mu	ext{F}$$

Question 19

Which of the following best describes the function of a resistor in an RC circuit?

Accepted Answer

It dissipates energy as heat.

Chapter 19: DC Circuits: Series and Parallel Circuits, Kirchhoff’s Rules, and RC Circuits

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