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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.
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, Irms = 0.1 A
Peak current (I0) 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 (UL) 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`
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