Question

An LC circuit has $L$ = 5mH and $C$ = 20$\mu$F. $v=5\times {10}^{-3}cos\omega t$ is supplied. $\omega$ is twice the resonant frequency. Find the maximum charge stored in the capacitor :

• A. 66.6 nC
• B. 11.3 nC
• C. 23.2 nC
• D. 33.3 nC

Answer 1

Answer: (D)

33.3 nC

$\omega =2{\omega }_0=2\times \frac{1}{\sqrt{LC}}=\frac{2\times {10}^4}{\sqrt{10}}$

$I=\frac{V}{X_L-X_C}=\frac{V}{\omega L-\frac{1}{\omega C}}=\frac{5\times {10}^{-3}}{\sqrt{{(10\sqrt{10}-2.5\sqrt{10})}^2}}$

$=\frac{5\times {10}^{-3}}{7.5\sqrt{10}}=2.1\times {10}^{-4}A$

$V_C=I{X}_C$

and $Q=C{V}_C=\frac{I}{C\omega }\times C$

$Q=\frac{I}{\omega }=\frac{2.1\times {10}^{-4}\times \sqrt{10}}{2\times {10}^4}=33.3nC$