Question

The inductor in a $L-C$ oscillation has a maximum potential difference of $16V$ across the inductor of $3mH$ and maximum energy of $160\mu J$. The value of capacitor in $L-C$ circuit is :

• A. $0.8\mu F$
• B. $0.625\mu F$
• C. $1.6\mu F$
• D. $1.25\mu F$

Answer 1

The correct option is D $1.25\mu F$

Given

Maximum energy, $E_{total}=160\mu J$

In L-C circuit

Maximum potential is equal for both inductor and capacitor.

Total Energy = Energy in capacitor + Energy in inductor

Total Energy = Maximum Energy in capacitor=Maximum Energy in inductor

$\frac{1}{2}C{V}^2=E_{total}$

$C=\frac{2\times E_{total}}{V^2}=\frac{2\times 160\times {10}^{-6}}{{16}^2}=1.25\times {10}^{-6}F$

Capacitance is $1.25\mu F$