Question

An $LC$ circuit contains a $20\,mH$ inductor and a $50\, \mu F$ capacitor with an initial charge of $10\, mC$. The resistance of the circuit is negligible. Let the instant at which the circuit which is closed be $t = 0$. At what time the energy stored is completely magnetic?

• A. $t = 0$
• B. $t= 1.54 \,ms$
• C. $t= 3.14 \,ms$
• D. $t= 6.28 \,ms$

Answer 1

Answer: (B)

$t= 1.54 \,ms$

Answer 2

At time $t=\frac{T}{4}$, energy stored is completely magnetic. $\therefore$ Time $t = \frac{T}{4}=\frac{2\pi\sqrt{LC}}{4} \Rightarrow t=\frac{\pi\sqrt{20\times10^{-3}\times50\times10^{-6}}}{2}$ $t=\frac{\pi\sqrt{1000\times10^{-9}}}{2}$ $=\frac{\pi\sqrt{1\times10^{-6}}}{2}$ $=1.57\,ms$