Q: Which of the following is the correct formula for the total resistance of three resistors $R_1$, $R_2$, and $R_3$ connected in parallel?

$\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$

Question 1

Which of the following best describes the direction of conventional current in a metallic conductor?

Accepted Answer

It flows from high potential to low potential, along the direction of the electric field.

Question 2

Given the equation for electrical current $I = \frac{\Delta Q}{\Delta t}$, what are the SI units for current?

Accepted Answer

Coulombs per second (C/s)

Question 3

A cylindrical wire has a length $L$ and cross-sectional area $A$. If the wire is made of a material with resistivity $\rho$, what is its resistance?

Accepted Answer

$R = \frac{\rho L}{A}$

Question 4

If the length of a wire is doubled and the cross-sectional area is halved, how does its resistance change?

Accepted Answer

It becomes four times greater.

Question 5

Which statement about Ohm's law is correct?

Accepted Answer

It states that $V = IR$ for materials where resistance $R$ is constant.

Question 6

A resistor has a potential difference of 24 V across it and a current of 0.24 A flows through it. What is its resistance?

Accepted Answer

$100 \Omega$

Question 7

Two identical metal rods, each of length $L$ and resistivity $\rho$, are welded together end to end. What is the resistance of the combined rod?

Accepted Answer

$2R = \frac{2\rho L}{A}$

Question 8

If a wire carries a current of 1.6 A, how many electrons pass through a cross-section of the wire every second? (Charge of electron $e = 1.602 	imes 10^{-19}$ C)

Accepted Answer

$1.0 	imes 10^{19}$

Question 9

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

Accepted Answer

$I = \frac{\mathcal{E}}{R + r}$

Question 10

In a parallel circuit with three resistors $R_1$, $R_2$, and $R_3$, which statement is true about the potential difference across each resistor?

Accepted Answer

The potential difference is the same across all three resistors.

Question 11

Three identical bulbs are connected in parallel to a battery. If the switch in the circuit is closed, what happens to the brightness of the bulbs?

Accepted Answer

All bulbs have the same brightness.

Question 12

If the resistance of a light bulb increases, what happens to the current through it for a fixed voltage?

Accepted Answer

The current decreases.

Question 13

A battery with emf $\mathcal{E} = 2.5$ V and internal resistance $r = 1000 \Omega$ supplies a current of $0.5$ mA. What is the terminal voltage?

Accepted Answer

$2.0$ V

Question 14

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 15

In a series circuit with three resistors, which statement is true about the current through each resistor?

Accepted Answer

The current is the same through all three resistors.

Question 16

A circuit contains a resistor of $R$ and another of $2R$ in series. If the power output as heat from the resistor $R$ is $20$ W, what is the power output of the resistor $2R$?

Accepted Answer

$10$ W

Question 17

A circuit contains a resistor of $R$ and another of $2R$ in parallel. If the power output as heat from the resistor $R$ is $20$ W, what is the power output of the resistor $2R$?

Accepted Answer

$40$ W

Question 18

If a switch in a parallel circuit is opened, what happens to the total resistance in the circuit?

Accepted Answer

It increases.

Question 19

Which of the following is the correct formula for the total resistance of three resistors $R_1$, $R_2$, and $R_3$ connected in parallel?

Accepted Answer

$\frac{1}{R_{	ext{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$

Current, Resistance, and DC Circuits – Study Notes

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