Question

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.

Answer 1

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 (I₀) is given by,

I₀ = `(E_rms sqrt 2)/Z`

= `(50 xx 1.4 xx 414)/(500)`

= 01414 A

Electrical energy stored in capacitor  is given by,

U_C = `1/2 CV^2`

⇒ U_C = `1/2 xx 20 xx 10^-6 xx 50 xx 50`

⇒ U_C = 25 × 10⁻³ J = 25 mJ

Magnetic field energy stored in the coil (U_L) is given by,

U_L = `1/2 LI_0^2`

⇒ U_L ≈ `1/2 xx 1 xx (0.1414)^2`

⇒ U_L ≈ 5 × 10⁻³ J

⇒ L = 5 mJ