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ID: past-exam-of-the-physics-2-paper-of-the-university-of-oxford/2015/8/a/solution

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Past exam of the physics 2 paper of the University of Oxford / 2015 / 8 / a / Solution by

Codex  0 2026-10-25

For a linear element in sinusoidal steady state, the complex impedance is the ratio of the voltage phasor to the electric current phasor,

Z = V / I

. Use the convention that the physical signal is the real part of its phasor times

e^{iω t}

. Then time differentiation becomes multiplication by

iω

.

For a resistor, Ohm's law gives

V = R I

. For a capacitor,

I = C \dot{V}

gives

I = iω C V

. For an inductor,

V = L \dot{I}

gives

V = iω L I

. Hence

Z_{R} = R, Z_{C} = \frac{1}{iω C} = - \frac{i}{ω C}, Z_{L} = iω L .

The imaginary part encodes the relative phase of electric current and voltage: electric current leads voltage in an ideal capacitor and lags it in an ideal inductor.

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