Q: A 2.00-nF capacitor with an initial charge of $$5.10\,\mu\text{C} is $$discharged through a $$1.30\,\text{k}\Omega$$ resistor. What is the time constant $$\tau$$ for this circuit?

$$\tau = RC = (1.30 \times 10^3$\,\Omega)(2.00 \times 10$$^{-9}$$\,\text{F}) = 2.60 \times 10$$^{-6}$$\,\text{s}$$

Question 1

Which of the following correctly describes the equivalent resistance $$R_{eq}$$ for three resistors $$R_1$$, $$R_2$$, and $$R_3$$ connected in series?

Accepted Answer

$$R_{eq} = R_1$ + R_2$ + R_3$

Question 2

Three resistors of $$12\,\Omega$$, $$6\,\Omega$$, and $$5\,\Omega$$ are connected as shown: the $$12\,\Omega$$ and $$6\,\Omega$$ resistors are in parallel, and this combination is in series with the $$5\,\Omega$$ resistor. What is the equivalent resistance between the endpoints?

Accepted Answer

$$R_{eq} = 9\,\Omega$$

Question 3

Which arrangement of three identical resistors $$R$$ results in the smallest equivalent resistance between two points?

Accepted Answer

All three resistors in parallel: $$R_{eq} = \frac{R}{3}$$

Question 4

A 120-V, 60-W light bulb, a 120-V, 120-W light bulb, and a 120-V, 240-W light bulb are connected in parallel to a 120 V source. Which bulb glows the brightest?

Accepted Answer

The 120-V, 240-W light bulb

Question 5

In a series circuit containing a battery, a resistor, and a capacitor, which of the following affects the maximum charge $$Q_{max}$$ stored on the capacitor?

Accepted Answer

Both the emf $$\mathcal{E} of $$the battery and the capacitance $$C of $$the capacitor

Question 6

A 2.00-nF capacitor with an initial charge of $$5.10\,\mu	ext{C} is $$discharged through a $$1.30\,	ext{k}\Omega$$ resistor. What is the time constant $$	au$$ for this circuit?

Accepted Answer

$$	au = RC = (1.30 	imes 10^3$\,\Omega)(2.00 	imes 10$$^{-9}$$\,	ext{F}) = 2.60 	imes 10$$^{-6}$$\,	ext{s}$$

Question 7

Which of the following statements about Kirchhoff’s rules is correct?

Accepted Answer

The junction rule is a consequence of charge conservation, and the loop rule is a consequence of energy conservation.

Question 8

A voltmeter is connected across a resistor in a circuit. Which of the following is true about the voltmeter?

Accepted Answer

It has a very high resistance so that it draws negligible current.

Question 9

A battery, a resistor, and a capacitor are connected in series. Which of the following affects the rate at which the capacitor charges?

Accepted Answer

Both the capacitance $$C$$ and the resistance $$R$$

Question 10

In a household power distribution system, why is it safer to use a three-prong plug for electrical appliances?

Accepted Answer

The third prong connects the appliance to ground, reducing the risk of electric shock.

Question 11

A circuit contains a $$12\,	ext{V}$$ battery, a $$3.9\,\Omega$$ resistor, a $$9.8\,\Omega$$ resistor, a $$1.2\,\Omega$$ resistor, a $$6.7\,\Omega$$ resistor, and a $$9.0\,	ext{V}$$ battery as shown in a multi-loop circuit. Which law would you use to write equations for the unknown currents?

Accepted Answer

Kirchhoff’s rules (junction and loop rules)

Question 12

Which of the following best describes the function of a fuse in a household circuit?

Accepted Answer

It melts and breaks the circuit if the current exceeds a safe value.

Question 13

A d’Arsonval galvanometer is used in the construction of which of the following instruments?

Accepted Answer

Both ammeters and voltmeters

Question 14

Which of the following is the correct expression for the power $$P$$ dissipated in a resistor $$R$$ when a current $$I$$ flows through it?

Accepted Answer

$$P = I^2$ R$$

Question 15

A capacitor is being charged in an RC circuit. Which of the following best describes the behavior of the current $$I$$ and the charge $$q on $$the capacitor over time?

Accepted Answer

The current decreases exponentially, and the charge increases exponentially toward a maximum value.

Question 16

Which of the following is the correct formula for the equivalent resistance $$R_{eq} of $$two resistors $$R_1$$ and $$R_2 in $$parallel?

Accepted Answer

$$\frac{1}{R_{eq}} = \frac{1}{R_1$} + \frac{1}{R_2$}$$

Question 17

A moving-coil ammeter is constructed by placing a shunt resistor $$R_{sh} in $$parallel with the galvanometer coil. What is the purpose of the shunt resistor?

Accepted Answer

To allow most of the current to bypass the galvanometer, preventing damage

Question 18

Which of the following best describes the function of a potentiometer in electrical measurements?

Accepted Answer

It measures the emf of a source without drawing any current from the source.

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

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