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AP Physics C: E&M
11.8 Resistor Capacitor (RC) Circuits
11.6 Kirchhoff’s Loop Rule
IntermediateMCQGraphicalMathematicalConceptual21k
A circuit schematic drawn with rectangular loops. On the far left, a vertical branch contains an ideal battery labeled \(\mathcal{E}\), with its longer line at the top and shorter line at the bottom. A bottom horizontal wire extends from the negative terminal of the battery to the right. From the positive terminal of the battery, a wire extends rightward to contact 1 of a single-pole double-throw switch labeled \(S\). The movable blade of switch \(S\) is connected to a node at terminal point \(a\). Contact 2 of the switch connects via a vertical wire downward to the bottom wire. From point \(a\), a horizontal wire leads through a resistor labeled \(R\) to terminal point \(b\). From point \(b\), a wire connects to the top horizontal plate of a capacitor labeled \(C\). The bottom horizontal plate of capacitor \(C\) connects to the bottom wire. No other labels, lines, text, or components appear.
Circuit schematic for charging and discharging the capacitor.
In the circuit shown, an ideal battery of EMF \(\mathcal{E}\) is connected to a resistor of resistance \(R\), an initially uncharged capacitor of capacitance \(C\), and a two-position switch \(S\). At time \(t = 0\), the switch is set to position 1 to charge the capacitor, and at time \(t = t_1\) (where \(t_1 \gg RC\)), the switch is moved to position 2 so that the capacitor discharges through the resistor. A voltage sensor continuously records the potential difference \(\Delta V_R = V_a - V_b\) across the resistor, where point \(a\) is to the left of the resistor and point \(b\) is between the resistor and the capacitor. Which of the following graphs best represents \(\Delta V_R\) as a function of time \(t\)?

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