 Solution

ID: past-exam-of-the-physics-2-paper-of-the-university-of-oxford/2014/5/i/solution

With phasors proportional to

e^{iω t}

Z = R + i (ω L - \frac{1}{ω C}), I_{0} = \frac{V _{0}}{R ^{2} + ( ω L - 1/ ( ω C ) ) ^{2}} .

For fixed

V_{0}

and frequency-independent positive

R

, the maximum occurs when the reactances cancel. Thus

ω_{0} = \frac{1}{L C}, I_{0, m a x} = \frac{V _{0}}{R} .

This is the driven current resonance; a damped free-oscillation frequency is a different quantity.

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