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AP Physics C: E&M
11.8 Resistor Capacitor (RC) Circuits
11.7 Kirchhoff’s Junction Rule
11.6 Kirchhoff’s Loop Rule
AdvancedMCQMathematicalConceptual22.5k
A single rectangular circuit schematic oriented horizontally. On the left vertical wire, a battery symbol is shown with a long line on top and a short thick line on bottom, labeled \(\mathcal{E}\) to its left. The wire continues upward to a top horizontal branch containing an open knife switch labeled \(S\) and a series resistor drawn as a zigzag segment labeled \(R\). The wire then splits at a right-hand junction into two parallel vertical branches before recombining at a bottom junction. The left parallel branch contains an ideal capacitor drawn as two parallel horizontal plates labeled \(C\). The right parallel branch contains a resistor drawn as a zigzag segment labeled \(R_L\). The recombined bottom wire runs horizontally back to the bottom of the battery. No other labels, lines, text, or axes appear.
Circuit schematic with a battery, series resistor, switch, and a parallel leaky capacitor model.
A real capacitor is modeled as an ideal capacitor of capacitance \(C\) connected in parallel with an internal leakage resistance \(R_L\).

This parallel combination is placed in series with an ideal battery of electromotive force \(\mathcal{E}\), an open switch \(S\), and an external resistor of resistance \(R\).

At time \(t = 0\), the switch is closed with the capacitor initially uncharged, resulting in a time-dependent charge of \(q(t) = \dfrac{C\mathcal{E} R_L}{R + R_L}\left(1 - e^{-t/\tau}\right)\), where \(\tau = \left(\dfrac{R R_L}{R + R_L}\right)C\).

Which of the following statements correctly describes the physical behavior of the circuit in the specified limit?

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