AP Physics C Electricity and Magnetism · Question of the Day

AP Physics C Electricity and Magnetism Question of the Day

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Thursday, September 17, 2026

A circuit consists of an ideal battery connected to a resistor $R_1$ in series with a parallel combination of two other resistors, $R_2$ and $R_3$ .

If the resistance of $R_2$ is decreased, what is the effect on the potential difference across $R_3$ ?

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A circuit consists of an ideal battery connected to a resistor $R_1$ in series with a parallel combination of two other resistors, $R_2$ and $R_3$ .

If the resistance of $R_2$ is decreased, what is the effect on the potential difference across $R_3$ ?

It decreases, because the total resistance of the circuit decreases. (correct answer)
It increases, because the total current from the battery increases.
It decreases, because a smaller fraction of the total current will flow through $R_3$ .
It remains the same, because $R_3$ and the battery are unchanged.

Explanation: Decreasing $R_2$ decreases the equivalent resistance of the parallel combination ( $R_p$ ). This, in turn, decreases the total equivalent resistance of the circuit ( $R_{eq} = R_1 + R_p$ ). A lower total resistance causes the total current from the battery ( $I_{total}$ ) to increase. The potential difference across $R_1$ is $V_1 = I_{total}R_1$ , so $V_1$ increases. The potential difference across the parallel part (and thus across $R_3$ ) is given by Kirchhoff's loop rule: $V_p = V_3 = \mathcal{E} - V_1$ . Since $V_1$ increases, $V_3$ must decrease.