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AP Physics C: E&M
11.8 Resistor Capacitor (RC) Circuits
11.6 Kirchhoff’s Loop Rule
11.5 Compound Direct Current Circuits
AdvancedMCQMathematicalProportional Analysis23.7k
A circuit schematic containing a single-pole double-throw switch labeled \(S\). The common terminal of switch \(S\) connects to the top terminal of a capacitor labeled \(C\), whose bottom terminal connects to a continuous horizontal bottom wire. Position 1 of switch \(S\) is on the left, connecting to a vertical branch with an ideal battery labeled \(\mathcal{E}\) and a series resistor labeled \(R\), which connects to the bottom wire. Position 2 of switch \(S\) is on the right, connecting to a branch containing a resistor labeled \(R\) in series with a parallel pair of two identical resistors, each labeled \(R\), which then returns to the bottom wire. The switch lever is shown tilted toward position 1. No other labels, lines, text, or axes appear.
Circuit schematic with a two-position switch, capacitor, battery, and resistor network.
In the circuit shown, an uncharged capacitor of capacitance \(C\) is connected in series with an ideal battery of electromotive force \(\mathcal{E}\) and a resistor of resistance \(R\) when switch \(S\) is in position 1. At time \(t = 0\), the switch is moved to position 1. At time \(t_1 = RC \ln 2\), the switch is instantaneously moved to position 2, disconnecting the battery and connecting the capacitor to a discharging network composed of a resistor of resistance \(R\) in series with a parallel combination of two identical resistors, each of resistance \(R\). Immediately after the switch is moved to position 2, what is the magnitude of the time rate of change of the current discharging the capacitor, \(\left|\dfrac{dI}{dt}\right|\)?

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