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AP Physics C: E&M
11.8 Resistor Capacitor (RC) Circuits
11.6 Kirchhoff’s Loop Rule
IntermediateMCQMathematicalConceptual22.4k
A rectangular circuit schematic in grayscale. On the left vertical branch is an ideal battery represented by two parallel horizontal plates, the longer upper plate labeled with a plus sign, labeled \(\mathcal{E}\). Above the battery on the top horizontal wire is an open single-pole switch labeled \(S\). The top wire extends rightward to a junction node. From this node, two parallel branches run downward to a bottom junction node that connects back to the negative terminal of the battery. The first branch, labeled with an arrow pointing downward labeled \(I_1\), contains a resistor labeled \(R\) in series with a capacitor of two equal-length parallel horizontal plates labeled \(C\). The second branch, labeled with a downward arrow labeled \(I_2\), contains an upper resistor labeled \(R\) connected in series with a parallel sub-loop; the left path of this sub-loop contains a resistor labeled \(R\) and the right path contains a capacitor labeled \(C\). No other labels, lines, text, or axes appear.
Circuit schematic with battery, switch, resistors, and capacitors in two parallel branches.
In the circuit shown, an ideal battery of electromotive force \(\mathcal{E}\) is connected in series with an open switch \(S\). The switch is in series with two parallel branches. Branch 1 contains a resistor of resistance \(R\) connected in series with an initially uncharged capacitor of capacitance \(C\), carrying branch current \(I_1\), while Branch 2 contains a resistor of resistance \(R\) connected in series with a parallel combination of a second resistor of resistance \(R\) and a second initially uncharged capacitor of capacitance \(C\), carrying total branch current \(I_2\). Which of the following correctly indicates the current \(I_1\) immediately after switch \(S\) is closed, the current \(I_2\) immediately after switch \(S\) is closed, and the current \(I_2\) a long time after switch \(S\) is closed?

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