First slide

Electrical Resonance series circuit

Question

In a series circuit $C = 2\mu F,\,L = 1mH$ and $R = 10\,\Omega ,$ when the current in the circuit is maximum, at that time the ratio of the energies stored in the capacitor and the inductor will be

Moderate

A

1 : 1
B

1 : 2
C

2 : 1
D

1 : 5

Solution

Current will be maximum in the condition of resonance so ${i_{\max }} = \frac{V}{R} = \frac{V}{{10}}A$
Energy stored in the coil ${W_L} = \frac{1}{2}Li_{\max }^2 = \frac{1}{2}L{\left( {\frac{E}{{10}}} \right)^2}$
$= \frac{1}{2} \times {10^{ - 3}}\left( {\frac{{{E^2}}}{{100}}} \right) = \frac{1}{2} \times {10^{ - 5}}{E^2}\;joule$
$\therefore$ Energy stored in the capacitor
${W_C} = \frac{1}{2}C{E^2} = \frac{1}{2} \times 2 \times {10^{ - 6}}{E^2} = {10^{ - 6}}{E^2}\;joule$

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