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AP Physics C: Electricity and Magnetism Unit 3: Electric Circuits

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Unit 3: Electric Circuits

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Question 1

In a circuit with two parallel resistors $R_{1} = 6 Ω$ and $R_{2} = 3 Ω$ in series with $R_{3} = 4 Ω$ , connected to a $12 V$ ideal battery, the voltage across the parallel combination is:

V_{∥} = 4 V

V_{∥} = 6 V

V_{∥} = 8 V

V_{∥} = 12 V

Question 2

A resistor $R = 10 Ω$ is connected to a battery of EMF $E = 20 V$ and internal resistance $r = 2 Ω$ . The current through the circuit is:

I = 2 A

I = 5/3 A \approx 1.67 A

I = 10 A

I = 1 A

Question 3

Three resistors $R_{1} = 2 Ω$ , $R_{2} = 3 Ω$ , $R_{3} = 6 Ω$ are connected in parallel across a $12 V$ source. The total power delivered by the source is:

P = 132 W

P = 144 W

P = 16 W

P = 72 W

Question 4

An RC circuit has $R = 10 k Ω$ , $C = 20 μ F$ , and battery $V_{0} = 6 V$ . The switch is closed at $t = 0$ with $C$ initially uncharged. The energy dissipated in the resistor from $t = 0$ to $t \to \infty$ is:

E_{R} = \frac{1}{2} C V_{0}^{2} = 360 μ J

E_{R} = C V_{0}^{2} = 720 μ J

E_{R} = \frac{V _{0}^{2}}{2 R} = 1.8 \times 1 0^{- 3} J

E_{R} = 0

, because an ideal resistor stores no energy.

Question 5

Using Kirchhoff's current law at a node, if currents $I_{1} = 3 A$ and $I_{2} = 5 A$ flow into the node, and $I_{3}$ flows out, which of the following is the correct application of KCL?

I_{3} = I_{1} + I_{2} = 8 A

I_{3} = I_{1} - I_{2} = - 2 A

I_{3} = (I_{1} + I_{2}) /2 = 4 A

I_{3} = 0

, because current distributes evenly.

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Question 6

In the Wheatstone bridge circuit, resistors $R_{1}$ (top-left) and $R_{2}$ (top-right) form one pair of arms; $R_{3}$ (bottom-left) and $R_{X}$ (bottom-right) form the other. A galvanometer connects the midpoints. The bridge is balanced when:

R_{1} / R_{3} = R_{2} / R_{X}

R_{1} + R_{X} = R_{2} + R_{3}

R_{1} R_{2} = R_{3} R_{X}

R_{1} / R_{2} = R_{X} / R_{3}

Question 7

An ammeter has negligible resistance. A voltmeter has very high resistance. Which connection correctly measures the voltage across resistor $R_{2}$ in a series circuit containing $R_{1}$ and $R_{2}$ ?

A.Connect the voltmeter in parallel with

R_{2}

and the ammeter in series in the branch containing

R_{2}

.B.Connect both the voltmeter and ammeter in series with

R_{2}

.C.Connect the voltmeter in series with

R_{2}

and the ammeter in parallel with

R_{2}

.D.Connect both the voltmeter and ammeter in parallel with

R_{2}

Question 8

An RC circuit consists of a resistor $R = 200 k Ω$ and capacitor $C = 50 μ F$ connected in series with a battery $V_{0} = 10 V$ . The switch is closed at $t = 0$ with the capacitor initially uncharged. The voltage across the capacitor at time $t = τ = R C$ is:

V_{C} (τ) = V_{0} (1 - e^{- 1}) \approx 6.32 V

V_{C} (τ) = V_{0} / e \approx 3.68 V

V_{C} (τ) = V_{0} = 10 V

V_{C} (τ) = V_{0} /2 = 5 V

Question 9

An RC circuit with $R = 1 k Ω$ and $C = 10 μ F$ is driven by a square-wave voltage that steps from $0$ to $V_{0} = 10 V$ at $t = 0$ (with $C$ initially uncharged). The voltage across the capacitor at $t = 2 τ$ (where $τ = R C$ ) is:

V_{C} (2 τ) = V_{0} (1 - e^{- 2}) \approx 8.65 V

V_{C} (2 τ) = V_{0} (1 - e^{- 1/2}) \approx 3.94 V

V_{C} (2 τ) = 2 V_{0} (1 - e^{- 1}) \approx 12.6 V

V_{C} (2 τ) = V_{0} e^{- 2} \approx 1.35 V

Question 10

A resistor $R = 50 Ω$ dissipates power $P = 8 W$ . The current through it and the voltage across it are:

I = 0.4 A

;

V = 20 V

I = 4 A

;

V = 200 V

I = 0.04 A

;

V = 2 V

I = 0.16 A

;

V = 8 V

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Question 11

A fully charged capacitor $C = 100 μ F$ at voltage $V_{0} = 50 V$ is discharged through resistor $R = 500 Ω$ starting at $t = 0$ . The charge on the capacitor as a function of time is $Q (t) = Q_{0} e^{- t / τ}$ . The current through the resistor at $t = 0$ is:

I (0) = V_{0} / R = 0.10 A

I (0) = Q_{0} / R C = 0.10 A

(same value, but a different derivation — both are valid).C.

I (0) = 0

, because the current builds up from zero.D.

I (0) = V_{0} / (R + 1/ C) \approx 0.10 A

Question 12

In the circuit below, $E_{1} = 12 V$ , $E_{2} = 6 V$ , $R_{1} = 4 Ω$ , and $R_{2} = 2 Ω$ . The two batteries and resistors are in a single loop, with $E_{1}$ and $E_{2}$ opposing each other. Applying Kirchhoff's voltage law, the current (taking $E_{1}$ 's direction as positive) is:

I = 1 A

I = 3 A

I = - 1 A

I = 2 A

AP Physics C: Electricity and Magnetism Unit 3: Electric Circuits — Free with Answer Explanations | Test Practice Hub