Consider the situation of the previous problem. Find the average electric field energy stored in the capacitor and the average magnetic field energy stored in the coil.

#### Solution

Given:

Resistance in the LCR circuit, *R* = 300 Ω

Capacitance in the LCR circuit, *C* = 20 μF = 20 × 10^{−6} F

Inductance in the LCR circuit, *L* = 1 henry

Net impedance of the LCR circuit, *Z *= 500 ohm

RMS value of voltage, = 50 V

RMS value of current,* **I*_{rms} = 0.1 A

Peak current (I_{0}) is given by,

`I_0 = (E_rms sqrt2) /Z = (50xx 1.4xx414)/(500) = 01414 A`

Electrical energy stored in capacitor is given by,

`U_C = 1/2 CV^2`

`rArr U_C = 1/2 xx 20xx10^-6xx50xx50`

`rArr U_C = 25xx10^-3 J =25 mJ`

Magnetic field energy stored in the coil (U_{L}) is given by,

`U_L = 1/2 LI_0^2`

`rArr U_L = 1/2xx1xx(0.1414)^2`

`rArr U_L ≈ 5xx10^-3 J`

`rArr_L = 5 mJ`