First slide

Electrical Resonance series circuit

Question

In a series circuit $C = 4 μ F, L = 2 m H$ and $R = 20 Ω,$ 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

4 : 5
C

2 : 1
D

1 : 5

Solution

Current will be maximum in the condition of resonance so $i_{\max} = \frac{E}{R} = \frac{E}{20} A$
Energy stored in the coil $W_{L} = \frac{1}{2} L i_{\max}^{2} = \frac{1}{2} L {(\frac{E}{20})}^{2}$
$= \frac{1}{2} \times 2 \times 10^{- 3} (\frac{E^{2}}{400}) = \frac{1}{4} \times 10^{- 5} E^{2} j o u l e$
Energy stored in the capacitor
$W_{C} = \frac{1}{2} C E^{2} = \frac{1}{2} \times 4 \times 10^{- 6} E^{2} = 2 \times 10^{- 6} E^{2} j o u l e$ $E_{c} / E_{: L} = 4 : 5$

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