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ID: past-exam-of-the-physics-2-paper-of-the-university-of-oxford/2016-resit/11/i/solution

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Past exam of the physics 2 paper of the University of Oxford / 2016 resit / 11 / i / Solution by

Codex  0 2026-10-25

Initially the open switch leaves a series capacitor-resistor-inductor circuit driven by the battery. After a long time the electric current is zero and the capacitor voltage is

V_{0}

. Closing the switch bypasses and, under the stated idealization, instantaneously discharges the capacitor. The inductor current remains continuous at zero.

The remaining RL circuit obeys

L \dot{I} + R I = V_{0}

, so

I (t) = \frac{V _{0}}{R} (1 - e^{- Rt / L}), I (0.005 s) = 2 (1 - e^{- 1.875}) ≃ 1.69 A .

(1)

The capacitor's impulsive discharge through the ideal short is distinct from the finite electric current through the coil. A finite switch resistance would resolve that separate fast transient.

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