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AP Physics 2
11.8 Resistor-Capacitor (RC) Circuits
AdvancedMCQGraphicalConceptual17.8k
A schematic of a DC circuit containing an ideal battery labeled \Delta V_0 = 12 \text{ V}, an open switch S, a resistor R_1 = 10 \ \Omega, and a parallel combination of resistor R_2 = 20 \ \Omega and capacitor C = 50 \ \mu\text{F}. The battery, switch S, and resistor R_1 are in series in the main branch. The main branch then splits into two parallel branches: top branch contains resistor R_2 and bottom branch contains capacitor C. All components are labeled with variable names and values. No other labels appear.
Circuit schematic with battery, switch, resistor \(R_1\), and parallel network of \(R_2\) and \(C\).
A graph of potential difference V_C across the capacitor in volts versus time t in microseconds. The vertical axis ranges from 0 to 12 V with grid lines at 0, 2, 4, 6, 8, 10, and 12 V. A horizontal dashed line at V_C = 8.0 \text{ V} is labeled '8.0 V'. The horizontal axis ranges from 0 to 1000 microseconds. A smooth curve begins at (0,0), rises steeply initially, and asymptotically approaches the 8.0 V line. At time t = 333 microseconds, a point on the curve is highlighted with a vertical dashed line down to the axis labeled \tau = 333 \ \mu\text{s} and a horizontal dashed line to the vertical axis at 5.0 V. No other labels appear.
Graph of potential difference \(V_C\) across the capacitor as a function of time \(t\).
In the circuit shown, an ideal battery of potential difference \(\Delta V_0 = 12\text{ V}\) is connected in series with an open switch \(S\) and resistor \(R_1 = 10\text{ }\Omega\). A parallel combination consisting of resistor \(R_2 = 20\text{ }\Omega\) and an initially uncharged capacitor \(C = 50\text{ }\mu\text{F}\) is connected in series with \(R_1\). At time \(t = 0\), switch \(S\) is closed, and the potential difference \(V_C\) across the capacitor is recorded as a function of time \(t\), producing the graph shown. Which of the following statements correctly interprets the features of the graph regarding the circuit's behavior?

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