A capacitor of capacitance C has initial charge Q0 and connected to an inductor of inductance L as shown. At t=0 switch S is closed. The current through the inductor when energy in the capacitor is three times the energy of inductor is

Question

A capacitor of capacitance C has initial charge Q0 and connected to an inductor of inductance L as shown. At t=0 switch S is closed. The current through the inductor when energy in the capacitor is three times the energy of inductor is (A) (Q0/2 √L C) (B) (Q0/√L C) (C) (2 Q0/√L C) (D) (4 Q0/√L C)

Tardigrade Admin · Accepted Answer

E text total =Ei+Ec=(Q02/2 C) 4 Ei=(Q02/2 C) Ei=(Q02/8 C)=(1/2) L i2 i2=(Q02/4 L C) i=(Q0/2 √L C)

Q. A capacitor of capacitance $C$ has initial charge $Q_{0}$ and connected to an inductor of inductance $L$ as shown. At $t = 0$ switch $S$ is closed. The current through the inductor when energy in the capacitor is three times the energy of inductor is

$\frac{Q _{0}}{2 L C}$

$\frac{Q _{0}}{L C}$

$\frac{2 Q _{0}}{L C}$

$\frac{4 Q _{0}}{L C}$

$E_{total} = E_{i} + E_{c} = \frac{Q _{0}^{2}}{2 C}$
$4 E_{i} = \frac{Q _{0}^{2}}{2 C}$
$E_{i} = \frac{Q _{0}^{2}}{8 C} = \frac{1}{2} L i^{2}$
$i^{2} = \frac{Q _{0}^{2}}{4 L C}$
$i = \frac{Q _{0}}{2 L C}$

Q. A capacitor of capacitance C has initial charge Q0​ and connected to an inductor of inductance L as shown. At t=0 switch S is closed. The current through the inductor when energy in the capacitor is three times the energy of inductor is

2LC​Q0​​

LC​Q0​​

LC​2Q0​​

LC​4Q0​​