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AP Physics C: E&M
11.8 Resistor Capacitor (RC) Circuits
11.6 Kirchhoff’s Loop Rule
11.5 Compound Direct Current Circuits
IntermediateMCQMathematicalConceptual24.5k
A schematic diagram of a rectangular circuit with an ideal battery of emf \(\mathcal{E}\) on the left vertical wire, positive terminal upward, connected in series with an open switch \(S\) on the top horizontal wire. To the right of the switch, the circuit splits at an input junction into two parallel horizontal paths that recombine at a right vertical ground wire connected to the negative terminal. The upper path consists of two identical resistors labeled \(R\) in series, with node \(X\) labeled between them. The lower path consists of a resistor labeled \(R\) in series with node \(Y\), followed by two parallel branches: a top branch containing a resistor labeled \(R\) and a bottom branch containing a capacitor labeled \(C\). A vertical segment connects node \(X\) and node \(Y\), containing a central resistor labeled \(R\). No other labels, lines, text, or symbols appear.
Circuit diagram of a bridge network containing five resistors, an uncharged capacitor, an open switch, and an ideal battery.
In the circuit shown, an ideal battery of emf \(\mathcal{E}\) is connected in series with an open switch \(S\) across a bridge network. The upper path has two resistors of resistance \(R\) connected in series at node \(X\), while the lower path has a resistor of resistance \(R\) connected at node \(Y\) to a parallel pair consisting of another resistor of resistance \(R\) and an initially uncharged capacitor of capacitance \(C\). A central resistor of resistance \(R\) connects node \(X\) and node \(Y\). Which of the following correctly describes the potential difference \(\Delta V\) across the central resistor immediately after the switch is closed (\(t = 0\)) and long after the switch has been closed (\(t \to \infty\))?

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