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AP Physics 2
11.8 Resistor-Capacitor (RC) Circuits
11.5 Compound Direct Current (DC) Circuits
AdvancedMCQGraphicalMathematicalProportional AnalysisConceptual24.6k
A schematic of an electric circuit. On the left vertical branch is a DC voltage source labeled \(\varepsilon = 12.0\text{ V}\). Along the top horizontal wire is an open switch \(S\) followed in series by a resistor labeled \(R_1 = 100\text{ }\Omega\). To the right of \(R_1\), the circuit splits into two parallel vertical branches: the inner branch contains a resistor labeled \(R_2\), and the outer branch contains an uncharged capacitor labeled \(C\). All branches reconnect along the bottom horizontal wire back to the negative terminal of the source. No other text or components appear.
Circuit schematic
A graph of potential difference across the capacitor \(V_C\text{ (V)}\) versus time \(t\text{ (ms)}\). The vertical axis goes from \(0\) to \(10.0\text{ V}\) with gridlines every \(2.0\text{ V}\). A horizontal dashed line at \(V_C = 8.0\text{ V}\) represents the maximum asymptotic voltage. The horizontal axis goes from \(0\) to \(10.0\text{ ms}\) with gridlines every \(2.0\text{ ms}\). An exponential curve begins at \((0,0)\) and rises toward \(8.0\text{ V}\). A vertical dashed line indicates that at \(t = 2.0\text{ ms}\), the voltage reaches \(5.1\text{ V}\), which corresponds to one time constant \(\tau\). No other labels appear.
Voltage across capacitor vs. time
A circuit contains an ideal battery of electromotive force \(\varepsilon = 12.0\text{ V}\), a resistor \(R_1 = 100\text{ }\Omega\), an unknown resistor \(R_2\), an uncharged capacitor of capacitance \(C\), and a switch \(S\). As shown in the circuit schematic, \(R_1\) is in series with the battery loop, while \(R_2\) and \(C\) form parallel branches. The switch is closed at time \(t = 0\), and the potential difference across the capacitor \(V_C\) as a function of time \(t\) is recorded in the graph. Based on the circuit setup and the graph, what is the capacitance \(C\)?

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