In an oscillating LC circuit, the maximum charge on the capacitor is Q. When the energy is stored equally between the electric and magnetic fields, the charge on the capacitor is q. The relation betwe

Question

In an oscillating LC circuit, the maximum charge on the capacitor is Q. When the energy is stored equally between the electric and magnetic fields, the charge on the capacitor is q. The relation between Q and q is

TestHub · Accepted Answer

Total energy of the LC circuit is given by the maximum energy stored in the capacitor:

$U_{t o t a l} = \frac{Q ^{2}}{2 C}$

When the energy is stored equally between the electric and magnetic fields, the electric energy $U_{E}$ is half of the total energy:

$U_{E} = \frac{1}{2} U_{t o t a l}$

The electric energy at this instant is given by:

$U_{E} = \frac{q ^{2}}{2 C}$

Equating the expressions for $U_{E}$ :

$\frac{q ^{2}}{2 C} = \frac{1}{2} (\frac{Q ^{2}}{2 C})$

$q^{2} = \frac{Q ^{2}}{2}$

$Q = 2 q$

Answer: $Q = 2 q$

Physics - SHM Question with Solution | TestHub

Options:

Doubts & Discussion