An LC circuit contains a 20 mH inductor and a 50 μ 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?

Question

An LC circuit contains a 20 mH inductor and a 50 μ 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

Tardigrade Admin · Accepted Answer

At time t=(T/4), energy stored is completely magnetic. ∴ Time t = (T/4)=(2π√LC/4) ⇒ t=(π√20×10-3×50×10-6/2) t=(π√1000×10-9/2) =(π√1×10-6/2) =1.57 ms

Q. An $L C$ circuit contains a $20 m H$ inductor and a $50 μ F$ capacitor with an initial charge of $10 m C$ . 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?

$t = 0$

$t = 1.54 m s$

$t = 3.14 m s$

$t = 6.28 m s$

At time $t = \frac{T}{4}$ , energy stored is completely magnetic.
$∴$ Time $t = \frac{T}{4} = \frac{2 π L C}{4} \Rightarrow t = \frac{π 20 \times 1 0 ^{- 3} \times 50 \times 1 0 ^{- 6}}{2}$
$t = \frac{π 1000 \times 1 0 ^{- 9}}{2}$
$= \frac{π 1 \times 1 0 ^{- 6}}{2}$
$= 1.57 m s$

Q. An LC circuit contains a 20mH inductor and a 50μF capacitor with an initial charge of 10mC. 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?

t=0

t=1.54ms

t=3.14ms

t=6.28ms