In a series LCR circuit, the impedance is 10 and the rms current flowing through it is 5 A . The rms voltages across the resistor and the inductor are 30 V and 50 V , respectively. If the voltage across the capacitor is greater than the voltage across the inductor, the rms voltage across the capacitor is:

Step-by-step solution

The rms voltage of the source is given by Ohm's law for the entire circuit: V_ rms = Z I_ rms = 10 5 = 50 V Using the phasor addition formula for voltages in a series LCR circuit: V_ rms ^2 = V_R^2 + (V_C - V_L)^2 Substituting the known values: 50^2 = 30^2 + (V_C - 50)^2 2500 = 900 + (V_C - 50)^2 (V_C - 50)^2 = 1600 Taking the square root on both sides: V_C - 50 = 40 This gives two possible values for V_C : V_C = 50 + 40 = 90 V or V_C = 50 - 40 = 10 V Since it is given that the voltage across the capacitor is great