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AP Physics C: E&M
11.8 Resistor Capacitor (RC) Circuits
11.5 Compound Direct Current Circuits
AdvancedMCQMathematicalConceptual14.7k
A rectangular circuit schematic drawn in grayscale lines. On the left vertical branch sits a capacitor symbol labeled C. The top and bottom horizontal wires connect this left branch to a central vertical branch containing a resistor symbol labeled R. Extending further to the right, the top and bottom wires continue to form a parallel right vertical branch containing a circle with a capital letter V inside, labeled as having internal resistance R_V. A closed switch symbol is shown on the top wire between the capacitor and the central resistor branch. Direction arrows are omitted. All wire lines are solid black on a white background. No other labels, lines, text, or components appear.
Circuit schematic showing the capacitor discharging through resistor \(R\) and parallel voltmeter.
A capacitor of unknown capacitance \(C\) is initially charged to a potential difference \(V_0\) and then allowed to discharge through a resistor of known resistance \(R\). A student records the potential difference \(V\) across the capacitor as a function of elapsed time \(t\) using a voltmeter with a known, finite internal resistance \(R_V\) connected in parallel with the capacitor. To determine \(C\), the student linearizes the data by plotting \(\ln V\) on the vertical axis versus \(t\) on the horizontal axis, obtaining a best-fit line with a slope of magnitude \(S\). Which of the following expressions correctly yields the capacitance \(C\) in terms of \(S\), \(R\), and \(R_V\)?

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