Q. 184.5( 4 Votes )

A circuit contain

Answer :

Given: L = 80 mH = 80 × 10-3 H

capacitor C = 60 Μf = 60 × 10-6 F


Voltage V = 230 V


Frequency v = 50Hz


(a) Peak voltage is given by the formula:


V0 = V/√ 2


V0 = 230√2 V



Substituting the values we get



On calculating, we get


I0 = -11.63 A.


The amplitude of maximum current is given by the following relation:


I0 = 11.63 A.


The root mean square value of the current I = I0/√ 2


I = -11.63(A)/√ 2


I = - 8.22 A


(b) The potential difference across the inductor can be calculated as follows:


VL = I × ω × L = 8.22(A) × 100 π(Hz) × 80 × 10-3 (F) = 206.61 V


Potential difference across the capacitor is given by the formula as follows:


Vc = I × 1/ωC


Substituting values we get


Vc = 8.22(A) × 1/ 100 π(Hz) × 60 × 10-6(F)


On calculating, we get


Vc = 436.3 V


(c) Since the actual voltage leads the current by π/2, so the average power consumed by the inductor is zero.


(d) Since voltage lags the current by π/2, so the average power consumed by the capacitor is zero.


(e) The total power over a complete cycle is zero.


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