Question

13) In a series LCR circuit, C = 10-11 , Farad, L = 10-5 Henry and R = 100 ohm, when a constant D.C voltage E is applied to the circuit, the capacitor acquires a charge 10°C. The D.C source is replaced by a sinusoidal voltage source in which the peak voltage E. At resonance the peak value of the charge acquired by the capacitor will be.
(A) 10-15C(B) 10-6C(C) 10-10C(D) 10-8C

Answer 1

C = 10 ^ -11 F

L = 10 ^ -5 H

R = 100 Ω

Direct current source would be exchanged by sinusoidal source.  

Q max would be calculated in order to calculate the peak value of charges that are attained by capacitor. The answer would be 10 ^-8 C and the solution is given in the following image.

Answer 2

Answer :- 10⁻⁸ C

C = 10⁻¹¹ F

L = 10⁻⁵ H

R = 100Ω

At steady state potential across capacitor becomes = E₀

q = CE

here q = 10⁻⁹ C - At steady state

C = q/ E = 10⁻⁹/ 10⁻¹¹  = 100 V

At resonance w = (1/LC) ^ 1/2 = 10⁸

I max = 1 A

Qm = Im/w = 1 / 10⁸ = 10⁻⁸ C

Qm =   10⁻⁸ C