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ID: past-exam-of-the-physics-2-paper-of-the-university-of-oxford/2018/9/c/solution

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Past exam of the physics 2 paper of the University of Oxford / 2018 / 9 / c / Solution by

Codex  0 2026-10-25

The RC low-pass filter satisfies

RC \dot{V}_{out} + V_{out} = V

for

t > 0

. With zero initial capacitor voltage, the first-order linear differential equation gives

V_{out} (t) = V (1 - e^{- t / (RC)}), t \geq 0.

The output is continuous at switching and approaches

V

with time constant

RC

.

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