A coil of self -inductance 0.16 H is connected to a condenser of capacity 0.81 $π$ F. What should be the frequency of alternating current that should be applied so that there is resonance in the circuit? Resistance of circuit is negligible.

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Solution

Given,
Self inductance, L = 0.16 H
Capacitance, C = 0.81

π

(a) Frequency of the alternating current, v = \frac{1}{2 π \sqrt{LC}} = \frac{1}{2 \times 3.14 \sqrt{0.16 \times 0.81 \times 10^{- 6}}} Hz = \frac{1000}{6.28 \times 0.36} Hz = 442.3 Hz (b) Energy stored in the circuit, U = \frac{Q^{2}}{2 C} = \frac{36 \times 10^{- 6}}{2 \times 0.81 \times 10^{- 6}} J = 22.2 J

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