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 instantaneous charge on the capacitor ‘q’ is ______.

Options

• Q

• `Q/2`

• `Q/sqrt 2`

• `Q/sqrt 3`

Answer 1

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 instantaneous charge on the capacitor ‘q’ is `bbunderline(Q/sqrt 2)`.

Explanation:

Maximum energy stored in a capacitor (E₁) = `Q^2/(2 C)`

When energy is stored equally between the electric and magnetic fields, then energy in the capacitor is:

E₂ = `q^2/(2 )`

Given q is the instantaneous charge on the capacitor.

⇒ E₂ = `q^2/(2C)`

∴ `q^2/(2C) = 1/2 Q^2/(2C)`

q' = `Q/sqrt 2`