Series LCR circuit containing an a.c. source of 100V has a inductor and a capacitor of reactance 24 and 16 respectively. If a resistance of 6 is connected in series, then the potential difference across the series combination of inductor and capacitor only is

Step-by-step solution

Given V = 100 V , X_L = 24 , X_C = 16 , and R = 6 . The net reactance of the circuit is X = X_L - X_C = 24 - 16 = 8 . The impedance of the series LCR circuit is given by Z = R^2 + (X_L - X_C)^2 . Substituting the values, Z = 6^2 + 8^2 = 36 + 64 = 10 . The rms current in the circuit is I = V Z = 100 10 = 10 A . The potential difference across the series combination of the inductor and capacitor is V_ LC = I |X_L - X_C| . V_ LC = 10 8 = 80 V .