Question 1

Which of the following statements best describes the current through each resistor in a series circuit, as shown in the first image?

Accepted Answer

The same current flows sequentially through each resistor.

Question 2

Given two resistors, $$R_1$$ and $$R_2$$, connected in parallel as shown in the second image, what is the correct formula for the equivalent resistance $$R_{eq}$$?

Accepted Answer

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

Question 3

If three resistors, each of $$10\,\Omega$$, are connected in series as shown in the first image, what is the total resistance?

Accepted Answer

$$30\,\Omega$$

Question 4

In a parallel circuit (second image), if $$\Delta V is $$the voltage across each resistor, what is the current through a resistor $$R$$?

Accepted Answer

$$i = \frac{\Delta V}{R}$$

Question 5

A battery with emf $$V_0$$ and internal resistance $$r is $$connected to an external resistor $$R. $$What is the expression for the current $$i in $$the circuit?

Accepted Answer

$$i = \frac{V_0$}{R + r}$$

Question 6

If the battery in the last image is disconnected from the circuit (open circuit), what is the voltage measured across its terminals?

Accepted Answer

$$V_0$$

Question 7

Which of the following is true about the voltage drop across the internal resistance of a battery when no current flows?

Accepted Answer

The voltage drop is zero.

Question 8

A circuit contains three resistors in parallel: $$R_1 = 2$$\,\Omega$$, R_2$ = 3\,\Omega$$, and $$R_3 = 6$$\,\Omega$$. What is the equivalent resistance?

Accepted Answer

$$R_{eq} = 1\,\Omega$$

Question 9

If the total current entering a parallel circuit is $$I$$, and the resistors are $$R_1$$ and $$R_2$$, which equation correctly relates the total current to the branch currents?

Accepted Answer

$$I = i_1$ + i_2$

Question 10

A real battery is modeled as an ideal battery in series with a resistor. If the external circuit draws a current $$i$$, what is the terminal voltage $$\Delta V$$?

Accepted Answer

$$\Delta V = V_0$ - ri$$

Question 11

Which configuration (series or parallel) is best for minimizing the total resistance in a circuit with multiple resistors?

Accepted Answer

Parallel

Question 12

If you double the number of identical resistors in series, what happens to the total resistance?

Accepted Answer

It doubles.

Question 13

If you double the number of identical resistors in parallel, what happens to the total resistance?

Accepted Answer

It is halved.

Question 14

A wire is made of two coaxial conductors with different resistivities. Which factor does NOT affect the total resistance?

Accepted Answer

The color of the wire

Question 15

A $$12\,	ext{V}$$ battery with internal resistance $$0.5\,\Omega is $$connected to a $$5.5\,\Omega$$ load. What is the current in the circuit?

Accepted Answer

$$1.85\,	ext{A}$$

Question 16

Which of the following best explains why the voltage across a battery drops when a large current is drawn?

Accepted Answer

The internal resistance causes a larger voltage drop ($$ri).$$

Question 17

If a circuit contains a $$100\,\Omega$$ resistor and a $$200\,\Omega$$ resistor in parallel, what is the equivalent resistance?

Accepted Answer

$$66.7\,\Omega$$

Question 18

Which of the following is a correct statement about the potential difference across resistors in parallel?

Accepted Answer

It is the same for all resistors.

Question 19

A circuit contains a $$120\,\Omega$$ and a $$360\,\Omega$$ resistor in series. What is the total resistance?

Accepted Answer

$$480\,\Omega$$

Question 20

Which of the following best describes the effect of negligible connecting wire resistance in circuit analysis?

Accepted Answer

It allows us to ignore the wires' resistance in calculations.

Resistors in Series and Parallel, and Battery Internal Resistance

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