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AP Physics C: E&M
11.8 Resistor Capacitor (RC) Circuits
IntermediateMCQMathematicalProportional Analysis21.2k
A schematic diagram of a DC circuit. At the top left, an ideal battery labeled V_0 is oriented vertically with its positive terminal on top. Connected to the positive terminal, a top horizontal wire extends to the right, containing an open switch labeled S, followed by a resistor labeled R_1 = R. The wire reaches a top junction node. From this node, two parallel vertical branches descend to a bottom junction node. The left branch contains a resistor labeled R_2 = 2R in series above an uncharged capacitor labeled C. The right branch contains a resistor labeled R_3 = 2R. A single bottom horizontal wire connects the bottom junction node back to the negative terminal of the battery. No other labels, lines, text, or axes appear.
Circuit schematic with switch S, battery V_0, resistors R_1, R_2, R_3, and capacitor C.
An ideal battery of potential difference \(V_0\) is connected in series with an open switch \(S\) and a resistor \(R_1 = R\). This combination is connected across a parallel network consisting of two branches: Branch 1 contains a resistor \(R_2 = 2R\) in series with an initially uncharged capacitor \(C\), and Branch 2 contains a resistor \(R_3 = 2R\). At time \(t = 0\), switch \(S\) is closed. Which row in the table correctly identifies the initial current \(I_3(0^+)\) through resistor \(R_3\) immediately after the switch is closed, and describes the behavior of current \(I_3(t)\) for \(t > 0\)?

RowInitial Current \(I_3(0^+)\)Behavior of \(I_3(t)\) for \(t > 0\)
Row A\(\dfrac{V_0}{2R}\)Exponentially decreases toward zero
Row B\(\dfrac{V_0}{4R}\)Exponentially decreases toward zero
Row C\(\dfrac{V_0}{4R}\)Exponentially increases toward \(\dfrac{V_0}{3R}\)
Row D\(\dfrac{V_0}{3R}\)Exponentially decreases toward \(\dfrac{V_0}{4R}\)

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