Q: In a circuit, the sum of the currents entering a junction is 5 A. If two wires leave the junction carrying 2 A and 1 A, what is the current in the third wire leaving the junction?

$$I_3 = 5$$\ \text{A} - 2\ \text{A} - 1\ \text{A} = 2\ \text{A}$$

Q: A loop in a circuit contains a battery of $$\varepsilon = 9\ \text{V}$$ and two resistors, $$R_1 = 2$$\ \Omega$$ and R_2$ = 1\ \Omega$$, in series. What is the current in the loop according to Kirchhoff’s loop rule?

$$I = \frac{\varepsilon}{R_1$ + R_2$} = \frac{9}{3} = 3\ \text{A}$$

Q: Three capacitors, $$C_1 = 2$$\ \mu\text{F}$$, C_2$ = 3\ \mu\text{F}$$, and $$C_3 = 5$$\ \mu\text{F}$$, are connected in parallel. What is the equivalent capacitance?

$$C_{eq} = C_1$ + C_2$ + C_3$ = 2 + 3 + 5 = 10\ \mu\text{F}$$

Q: A household circuit operates at $$120\ \text{V}. If a $$person with a body resistance of $$1,000\ \Omega$$ accidentally becomes part of the circuit, what is the current through the body?

$$I = \frac{V}{R} = \frac{120}{1000} = 0.12\ \text{A} = 120\ \text{mA}$$

Question 1

A battery with an emf of $$\varepsilon = 12\ 	ext{V}$$ and internal resistance $$r = 1\ \Omega is $$connected to an external resistor $$R = 5\ \Omega. $$What is the terminal voltage of the battery when current is flowing?

Accepted Answer

$$V = \varepsilon - Ir$$,\ where\ I = \frac{\varepsilon}{R + r} = \frac{12}{6} = 2\ 	ext{A},\ V = 12 - 2 	imes 1 = 10\ 	ext{V}$

Question 2

Three resistors, $$R_1 = 2$$\ \Omega$$, R_2$ = 4\ \Omega$$, and $$R_3 = 6$$\ \Omega$$, are connected in series. What is the equivalent resistance?

Accepted Answer

$$R_{eq} = R_1$ + R_2$ + R_3$ = 2 + 4 + 6 = 12\ \Omega$$

Question 3

Two resistors, $$R_1 = 3$$\ \Omega$$ and R_2$ = 6\ \Omega$$, are connected in parallel. What is the equivalent resistance?

Accepted Answer

$$\frac{1}{R_{eq}} = \frac{1}{R_1$} + \frac{1}{R_2$} = \frac{1}{3} + \frac{1}{6} = \frac{1}{2} \Rightarrow R_{eq} = 2\ \Omega$$

Question 4

In a circuit, the sum of the currents entering a junction is 5 A. If two wires leave the junction carrying 2 A and 1 A, what is the current in the third wire leaving the junction?

Accepted Answer

$$I_3 = 5$$\ 	ext{A} - 2\ 	ext{A} - 1\ 	ext{A} = 2\ 	ext{A}$$

Question 5

A loop in a circuit contains a battery of $$\varepsilon = 9\ 	ext{V}$$ and two resistors, $$R_1 = 2$$\ \Omega$$ and R_2$ = 1\ \Omega$$, in series. What is the current in the loop according to Kirchhoff’s loop rule?

Accepted Answer

$$I = \frac{\varepsilon}{R_1$ + R_2$} = \frac{9}{3} = 3\ 	ext{A}$$

Question 6

Two batteries, one with $$\$$varepsilon_1$$ = 6\ 	ext{V}$$ and another with $$\$$varepsilon_2$$ = 3\ 	ext{V}$$, are connected in series in the same direction. What is the total emf?

Accepted Answer

$$\varepsilon_{total} = \$$varepsilon_1$$ + \$$varepsilon_2$$ = 6 + 3 = 9\ 	ext{V}$$

Question 7

Three capacitors, $$C_1 = 2$$\ \mu	ext{F}$$, C_2$ = 3\ \mu	ext{F}$$, and $$C_3 = 5$$\ \mu	ext{F}$$, are connected in parallel. What is the equivalent capacitance?

Accepted Answer

$$C_{eq} = C_1$ + C_2$ + C_3$ = 2 + 3 + 5 = 10\ \mu	ext{F}$$

Question 8

Two capacitors, $$C_1 = 4$$\ \mu	ext{F}$$ and C_2$ = 6\ \mu	ext{F}$$, are connected in series. What is the equivalent capacitance?

Accepted Answer

$$\frac{1}{C_{eq}} = \frac{1}{C_1$} + \frac{1}{C_2$} = \frac{1}{4} + \frac{1}{6} = \frac{5}{12} \Rightarrow C_{eq} = \frac{12}{5} = 2.4\ \mu	ext{F}$$

Question 9

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

Accepted Answer

$$	au = RC$$

Question 10

A capacitor in an RC circuit is charged to a voltage $$V_0. $$After a time $$t = 	au$$, what fraction of the maximum charge $$Q_0$$ remains on the capacitor?

Accepted Answer

$$Q = Q_0$ \left(1 - e$$^{-1}$$\right) \approx 0.63 Q_0$

Question 11

A household circuit operates at $$120\ 	ext{V}. If a $$person with a body resistance of $$1,000\ \Omega$$ accidentally becomes part of the circuit, what is the current through the body?

Accepted Answer

$$I = \frac{V}{R} = \frac{120}{1000} = 0.12\ 	ext{A} = 120\ 	ext{mA}$$

Question 12

Why should an ammeter have very low resistance?

Accepted Answer

To minimize its effect on the circuit current, since it is connected in series.

Question 13

Why should a voltmeter have very high resistance?

Accepted Answer

To minimize its effect on the circuit, since it is connected in parallel.

Question 14

A battery with emf $$\varepsilon = 10\ 	ext{V}$$ and internal resistance $$r = 2\ \Omega is $$connected to a load resistor $$R = 8\ \Omega. $$What is the current in the circuit?

Accepted Answer

$$I = \frac{\varepsilon}{R + r} = \frac{10}{8 + 2} = 1\ 	ext{A}$$

Question 15

A circuit contains two resistors, $$R_1 = 10$$\ \Omega$$ and R_2$ = 20\ \Omega$$, in parallel. What is the total current if the circuit is connected to a $$30\ 	ext{V}$$ battery?

Accepted Answer

$$I_{total} = \frac{V}{R_1$} + \frac{V}{R_2$} = \frac{30}{10} + \frac{30}{20} = 3 + 1.5 = 4.5\ 	ext{A}$$

Question 16

A charged capacitor of $$C = 10\ \mu	ext{F} is $$discharged through a resistor $$R = 1\ 	ext{k}\Omega. $$How long does it take for the charge to drop to $$37\% of $$its initial value?

Accepted Answer

The time is equal to the time constant $$	au = RC = 1000 	imes 10 	imes 10$$^{-6}$$ = 0.01\ 	ext{s}$$

Question 17

Which of the following best describes the effect of faulty wiring and improper grounding in household circuits?

Accepted Answer

They increase the risk of electric shock and fire hazards.

Question 18

A circuit contains a battery, a resistor, and a capacitor in series. When the switch is closed, which statement best describes the voltage across the capacitor as a function of time?

Accepted Answer

$$V_C(t) = V_0$ \left(1 - e$$^{-t/RC}$$\right)$$,\ where\ $$V_0$$\ is\ the\ battery\ voltage.

DC Circuits: Principles, Components, and Measurement

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