A series LCR circuit is connected to an AC source of rms voltage 130 V . The circuit components have a resistance of 12 , an inductive reactance of 14 , and a capacitive reactance of 9 . What will be the reading of an ideal AC voltmeter connected strictly across the series combination of the inductor and the capacitor?

Step-by-step solution

First, calculate the net impedance Z of the series LCR circuit: Z = R^2 + (X_L - X_C)^2 Substitute the given values ( R = 12 , X_L = 14 , X_C = 9 ): Z = 12^2 + (14 - 9)^2 Z = 144 + 5^2 Z = 144 + 25 = 169 = 13 Next, find the rms current I_ rms flowing through the circuit using Ohm's law for AC circuits: I_ rms = V_ rms Z = 130 V 13 = 10 A An ideal AC voltmeter connected across the inductor and capacitor combination will measure the net rms voltage across them. The net reactance of the LC combination is: X_ LC = |X_L