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 magnetic fields is ______.

पर्याय

• `pisqrt"LC"`

• `pi/4sqrt"LC"`

• `2pisqrt"LC"`

• `sqrt"LC"`

Answer 1

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 magnetic fields is `underlinebb(pi/4sqrt"LC")`.

Explanation:

As ω² = `1/"LC"`​ or ω = `1/sqrt"LC"`​

Maximum energy stored in capacitor = `1/2​"Q"_0^2/"C"`​​

Let at any instant t, the energy be stored equally between electric and magnetic field. Then energy stored in electric field at instant t is

`1/2"Q"^2/"C"=1/2[1/2"Q"_0^2/"C"]`

or Q² = `"Q"_0^2/2`

or Q = `"Q"_0/sqrt2`

⇒ Q₀ cos ωt = `"Q"_0/sqrt2`

or ωt = `pi/4` or t = `pi/(4omega)`

= `pi/(4xx(1//sqrt"LC"))`

= `(pisqrt"LC")/4`