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AP Physics C: E&M
13.5 Circuits with Resistors and Inductors (LR Circuits)
13.4 Inductance
IntermediateMCQMathematicalConceptual13.4k
A circuit schematic showing a two-position single-pole double-throw switch S. The center common terminal of switch S connects to the top of a vertical inductor labeled L. On the left, switch terminal 1 connects to a series branch containing an ideal battery labeled \(\mathcal{E}\) with its positive terminal upward and a resistor labeled R_1. On the right, switch terminal 2 connects to a vertical branch containing a resistor labeled R_2. The bottoms of the battery branch, the inductor branch, and the R_2 branch all meet at a common horizontal bottom wire. A dashed arrow near switch S indicates moving the switch arm from contact 1 to contact 2. No other labels, lines, text, or axes appear.
Circuit schematic with a two-position switch, battery, inductor, and two resistors.
In the circuit shown, an ideal battery of EMF \(\mathcal{E}\) is connected in series with a two-position switch \(S\), a resistor of resistance \(R_1\), and an ideal inductor of inductance \(L\). The switch has been closed in position 1 for a long time so that the circuit has reached a steady state. At time \(t = 0\), the switch is instantaneously moved to position 2, disconnecting the battery and connecting the inductor directly across a second resistor of resistance \(R_2\) in an isolated closed loop. Which of the following expressions represents the magnitude of the potential difference \(V(t)\) across the resistor of resistance \(R_2\) as a function of time \(t\) for \(t > 0\)?

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