A fully charged capacitor C with initial charge q0 is connected to a coil of self inductance L at t=0 . The time at which the energy is stored equally between the electric and the magnetic fields is

Question

A fully charged capacitor C with initial charge q0 is connected to a coil of self inductance L at t=0 . The time at which the energy is stored equally between the electric and the magnetic fields is (A) √L C (B) π √L C (C) (π/4) √L C (D) 2 π √L C

Tardigrade Admin · Accepted Answer

q=q0 cos ω t energy is halved when q=(q0/√2) ⇒ ω t=(π/4) ⇒ (1/√L c) t=(π/4) ⇒ t=(π/4) √L c

Q. A fully charged capacitor $C$ with initial charge $q_{0}$ is connected to a coil of self inductance $L$ at $t = 0.$ The time at which the energy is stored equally between the electric and the magnetic fields is

$L C$

$π L C$

$\frac{π}{4} L C$

$2 π L C$

$q = q_{0} cos ω t$
energy is halved when $q = \frac{q _{0}}{2}$
$\Rightarrow ω t = \frac{π}{4}$
$\Rightarrow \frac{1}{L c} t = \frac{π}{4}$
$\Rightarrow t = \frac{π}{4} L c$

Q. A fully charged capacitor C with initial charge q0​ is connected to a coil of self inductance L at t=0. The time at which the energy is stored equally between the electric and the magnetic fields is

LC​

πLC​

4π​LC​

2πLC​