AP Physics C: Electricity and Magnetism Practice Quiz: Compound Direct Current Circuits

Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026

Test your understanding with short quizzes. This quiz has 16 questions to check your progress.

Question 1 of 16

Three resistors with resistances of 2 Ω, 4 Ω, and 6 Ω are connected in series. What is the equivalent resistance of this combination?

A)0.92 ΩB)4 ΩC)12 ΩD)24 Ω

All Questions (16)

Three resistors with resistances of 2 Ω, 4 Ω, and 6 Ω are connected in series. What is the equivalent resistance of this combination?

A) 0.92 Ω

B) 4 Ω

C) 12 Ω

D) 24 Ω

Correct Answer: C

According to the rule for resistors in series, the equivalent resistance is the sum of the individual resistances. Therefore, R_eq = R1 + R2 + R3 = 2 Ω + 4 Ω + 6 Ω = 12 Ω.

Two resistors, one 10 Ω and one 15 Ω, are connected in parallel. What is the equivalent resistance of this parallel combination?

A) 25 Ω

B) 12.5 Ω

C) 6 Ω

D) 1.67 Ω

Correct Answer: C

For resistors in parallel, the inverse of the equivalent resistance is the sum of the inverses of the individual resistances: 1/R_eq = 1/R1 + 1/R2. So, 1/R_eq = 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6. Therefore, R_eq = 6 Ω.

A battery has a stated electromotive force (EMF) of 12 V. When a circuit is connected and a current flows, the potential difference across the battery's terminals is measured to be 11.5 V. This observation is best explained by the battery having:

A) an incorrect EMF rating.

B) internal resistance.

C) a parallel capacitor.

D) zero resistance.

Correct Answer: B

A nonideal battery has internal resistance. When current (I) flows, there is a potential drop (Ir) across this internal resistance (r). This reduces the terminal voltage below the EMF (ΔV_terminal = E - Ir). The drop from 12 V to 11.5 V indicates the presence of internal resistance.

What is the defining characteristic of an ideal ammeter that allows it to measure current without significantly affecting the circuit?

A) Zero resistance

B) Infinite resistance

C) A very large internal battery

D) The ability to be connected in parallel

Correct Answer: A

Ideal ammeters have zero resistance. Since they are connected in series, any resistance they have would add to the total circuit resistance, thereby changing the current they are intended to measure. Zero resistance ensures they do not affect the current.

A nonideal battery with an EMF of 9.0 V and an internal resistance of 0.5 Ω is connected to a circuit, causing a current of 2.0 A to flow. What is the potential difference across the terminals of the battery?

A) 10.0 V

B) 9.0 V

C) 8.5 V

D) 8.0 V

Correct Answer: D

The terminal potential difference is given by the equation ΔV_terminal = E - Ir, where E is the EMF, I is the current, and r is the internal resistance. Plugging in the values: ΔV_terminal = 9.0 V - (2.0 A * 0.5 Ω) = 9.0 V - 1.0 V = 8.0 V.

Why must an ideal voltmeter have infinite resistance?

A) To allow maximum current to flow through it for an accurate reading.

B) To prevent any current from flowing through it, so it doesn't alter the potential difference it is measuring.

C) To match the resistance of the component it is measuring.

D) To minimize the power dissipated by the voltmeter.

Correct Answer: B

A voltmeter is connected in parallel with a circuit element. If it had a finite resistance, it would provide an alternate path for current, altering the overall circuit current and the potential difference across the element. Infinite resistance ensures no charge flows through the voltmeter, leaving the circuit undisturbed.

A 4 Ω resistor and a 12 Ω resistor are connected in parallel. This combination is then connected in series with a 5 Ω resistor. What is the total equivalent resistance of the circuit?

A) 21 Ω

B) 8 Ω

C) 3.67 Ω

D) 1.8 Ω

Correct Answer: B

First, calculate the equivalent resistance of the parallel part: 1/R_p = 1/4 + 1/12 = 3/12 + 1/12 = 4/12 = 1/3. So, R_p = 3 Ω. Next, add the series resistor: R_total = R_p + 5 Ω = 3 Ω + 5 Ω = 8 Ω.

When a new resistor is added in parallel to an existing set of parallel resistors, the total equivalent resistance will:

A) increase.

B) decrease.

C) remain the same.

D) become the average of all resistances.

Correct Answer: B

Adding a resistor in parallel creates an additional path for current to flow. This makes it 'easier' for the total current to flow, which means the overall or equivalent resistance of the circuit decreases. Mathematically, adding another term (1/Ri) to the sum for 1/R_eq,p will always increase the value of 1/R_eq,p, thus decreasing R_eq,p.

A nonideal battery with EMF E and internal resistance r is connected to a variable external resistor R. As the value of R is increased, what happens to the potential difference across the terminals of the battery?

A) It decreases because the current decreases.

B) It increases because the current decreases.

C) It remains constant at E.

D) It decreases because the voltage drop across R increases.

Correct Answer: B

The total resistance of the circuit is R_total = R + r. The current is I = E / (R + r). As R increases, the total resistance increases, and the current I decreases. The terminal voltage is V_terminal = E - Ir. Since I is decreasing, the term Ir becomes smaller, and the terminal voltage gets closer to the EMF, E. Therefore, the terminal voltage increases.

To measure the current flowing through a specific resistor in a circuit, an ammeter must be connected:

A) in parallel with the resistor.

B) in series with the resistor.

C) in parallel with the battery.

D) in series with the entire circuit, regardless of the resistor's location.

Correct Answer: B

Current is the flow of charge. To measure the flow through a component, the measuring device (ammeter) must be placed in the path of the flow, which is a series connection. This ensures all the current passing through the resistor also passes through the ammeter.

What is the potential difference across the terminals of a nonideal battery with EMF E and internal resistance r when no current is being drawn from it?

A) Zero

B) Infinite

C) Less than E

D) Equal to E

Correct Answer: D

The terminal voltage equation is ΔV_terminal = E - Ir. If no current is being drawn, then I = 0. The equation simplifies to ΔV_terminal = E - (0 * r) = E. This is also known as the open-circuit voltage.

Which of the following statements is always true for a set of resistors connected in series?

A) The potential difference is the same across each resistor.

B) The current is the same through each resistor.

C) The equivalent resistance is smaller than the smallest individual resistance.

D) The power dissipated is the same for each resistor.

Correct Answer: B

In a series circuit, there is only one path for the charge to flow. Therefore, the current must be the same through every component in the series circuit. The potential difference is divided among the resistors, and the equivalent resistance is the sum of all individual resistances.

A 6.0 V battery with a 0.2 Ω internal resistance is connected to a 5.8 Ω external resistor. What is the current flowing in the circuit?

A) 1.03 A

B) 1.00 A

C) 0.97 A

D) 1.06 A

Correct Answer: B

In this circuit, the internal resistance acts in series with the external resistor. The total resistance is R_total = R_external + r_internal = 5.8 Ω + 0.2 Ω = 6.0 Ω. Using Ohm's Law with the battery's EMF, the current is I = E / R_total = 6.0 V / 6.0 Ω = 1.00 A.

An ideal voltmeter is mistakenly connected in series with a 100 Ω resistor and a 12 V ideal battery. What will the voltmeter read?

A) 0 V

B) 6 V

C) 12 V

D) A value dependent on the resistor.

Correct Answer: C

An ideal voltmeter has infinite resistance. When placed in series, it makes the total circuit resistance infinite, causing the current to drop to zero. The voltmeter measures the potential difference between its terminals. Since no current flows, there is no voltage drop across the 100 Ω resistor (V=IR=0*100=0). Therefore, the voltmeter is effectively measuring the potential difference across the ideal battery, which is 12 V.

How does the equivalent resistance of a series circuit change if one of the resistors is removed?

A) It increases.

B) It decreases.

C) It remains the same.

D) It becomes zero.

Correct Answer: B

The equivalent resistance of a series circuit is the sum of all individual resistances (R_eq,s = ΣR_i). If a resistor is removed from the series, its resistance value is subtracted from the sum, causing the total equivalent resistance to decrease.

A circuit contains a nonideal battery connected to two identical resistors in parallel. If one of the parallel resistors is removed from the circuit, how will the terminal voltage of the battery change?

A) It will increase.

B) It will decrease.

C) It will remain the same.

D) It will drop to zero.

Correct Answer: A

Removing a parallel resistor increases the total equivalent resistance of the external circuit. According to Ohm's Law (I = E / R_total), a higher total resistance will cause a smaller total current (I) to be drawn from the battery. The terminal voltage is given by V_terminal = E - Ir. Since the current I has decreased, the voltage drop across the internal resistance (Ir) also decreases, causing the terminal voltage to increase.