Question 1

In a circuit, three resistors $$R_1$$, $$R_2$$, and $$R_3$$ are connected in series. If $$R_1 = 2$$\ \Omega$$, R_2$ = 4\ \Omega$$, and $$R_3 = 6$$\ \Omega$$, what is the equivalent resistance R$$_{eq}$$ of the combination?

Accepted Answer

$$R_{eq} = 12\ \Omega$$

Question 2

Two resistors, $$R_1 = 10$$\ \Omega$$ and R_2$ = 20\ \Omega$$, are connected in parallel. What is the equivalent resistance $$R_{eq}$$?

Accepted Answer

$$R_{eq} = 6.67\ \Omega$$

Question 3

A circuit contains a battery of emf $$\epsilon = 12\ 	ext{V}$$ and three resistors in series: $$R_1 = 2$$\ \Omega$$, R_2$ = 3\ \Omega$$, and $$R_3 = 5$$\ \Omega$$. What is the current I$ in the circuit?

Accepted Answer

$$I = 1.0\ 	ext{A}$$

Question 4

In a parallel circuit, $$R_1 = 5$$\ \Omega$$ and R_2$ = 10\ \Omega$$ are connected across a $$10\ 	ext{V}$$ battery. What is the total current $$I$$ supplied by the battery?

Accepted Answer

$$I = 3\ 	ext{A}$$

Question 5

Which statement about household wiring is correct?

Accepted Answer

Devices are connected in parallel, so each operates independently and on the same voltage.

Question 6

A circuit contains a resistor $$R = 10\ \Omega$$ and a capacitor $$C = 100\ \mu	ext{F} in $$series with a $$12\ 	ext{V}$$ battery. What is the time constant $$	au$$ for charging the capacitor?

Accepted Answer

$$	au = 0.001\ 	ext{s}$$

Question 7

When applying Kirchhoff’s junction rule at a node where $$I_1$$ enters and $$I_2$$ and $$I_3$$ leave, which equation is correct?

Accepted Answer

$$I_1$$ = $$I_2$$ + $$I_3$$

Question 8

A voltmeter is used to measure the potential difference across a resistor. How should it be connected?

Accepted Answer

In parallel with the resistor

Question 9

A capacitor in an RC circuit is initially uncharged. When the switch is closed, what is the initial current $$I_0$$?

Accepted Answer

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

Question 10

In a circuit with a fully charged capacitor, what is the current through the branch containing the capacitor under steady-state conditions?

Accepted Answer

The current is zero.

Question 11

A $$100\ \Omega$$ resistor and a $$200\ \Omega$$ resistor are connected in parallel. What is the equivalent resistance?

Accepted Answer

$$R_{eq} = 66.7\ \Omega$$

Question 12

Which of the following is a consequence of conservation of energy in a single-loop circuit?

Accepted Answer

The sum of the potential differences across all elements in the loop is zero.

Question 13

A circuit contains a $$12\ 	ext{V}$$ battery and two resistors, $$R_1 = 4$$\ \Omega$$ and R_2$ = 8\ \Omega$$, in series. What is the power dissipated in $$R_1$$?

Accepted Answer

$$P = 3\ 	ext{W}$$

Question 14

What is the effect of a short circuit in a household wiring system?

Accepted Answer

It causes a very large current, which opens the circuit breaker.

Question 15

If a $$10\ \Omega$$ resistor and a $$20\ \Omega$$ resistor are connected in series, and the circuit is powered by a $$30\ 	ext{V}$$ battery, what is the current through the circuit?

Accepted Answer

$$I = 1\ 	ext{A}$$

Question 16

Which device is used to measure current in a circuit and how should it be connected?

Accepted Answer

An ammeter, connected in series

Question 17

In an RC circuit, the charge on the capacitor as a function of time during charging is given by:

Accepted Answer

$$q(t) = C\epsilon (1 - e$$^{-t/RC}$$)$$

Question 18

What is the main function of a ground wire in electrical appliances?

Accepted Answer

To provide a low-resistance path to ground in case of a fault, preventing electric shock.

Question 19

A $$100\ \Omega$$ resistor and a $$200\ \Omega$$ resistor are connected in parallel. If the total current entering the junction is $$3\ 	ext{A}$$, what is the current through the $$100\ \Omega$$ resistor?

Accepted Answer

$$I_{100} = 2\ 	ext{A}$$

Direct-Current Circuits: Series, Parallel, Kirchhoff’s Rules, and RC Circuits

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