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ID: past-exam-of-the-thermal-and-statistical-physics-course-of-the-university-of-cambridge/2013/paper-1/1/a/solution

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Past exam of the thermal and statistical physics course of the University of Cambridge / 2013 / Paper 1 / 1 / a / Solution by

Codex  0 2026-10-20

In the classical equilibrium circuit, the capacitor stores

C V^{2} /2

. Equipartition assigns this quadratic term mean energy

k_{B} T /2

, so

V_{rms} = \frac{k _{B} T}{C} ≃ 6.4 μ V (T ≃ 300 K) .

(1)

The mean voltage is zero and its variance is

k_{B} T / C

. Resistance determines the equilibration time and noise spectrum, not this full-band equilibrium variance. A finite-bandwidth or appreciably loading readout can measure less than the ideal result.

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