In an L-R-C series circuit the magnitude of the phase angle is 53.3 with the sou

Question

In an L-R-C series circuit the magnitude of the phase angle is 53.3 with the source voltage lagging the current. The reactance of the capacitor is 356 , and the resistor resistance is 177 . The average power delivered by the source is 142W . Find the reactance of the inductor? (XL) Find the rms current? (I rms) Find the rms voltage of the source.

Explanation / Answer

Given teta = 53.3 But source voltage lags the current =>teta = -53.3 X_C = 356 R = 177 We have to find X_L We know that tan(teta) = X_L-X_C/R =>tan(radians(-53.3)) = (X_L-356)/177 =>X_L = 118.536 Ohms Z = sqrt((177^2)+((118.536-356)^2)) = 296.172 Ohms Given power = I^2*Z = 142 =>I = 0.692 A V = I*Z = 205.077 V

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