In a series LCR circuit connected to an AC source, the parameters are given as R = 300 , C = 20 F , L = 1.0 henry , E _ rms = 50 V , and = 50/ Hz . Determine the rms potential differences across the capacitor, the resistor, and the inductor, respectively. (Observe that the sum of the rms potential differences across the three elements exceeds the rms voltage of the source.)

Step-by-step solution

The angular frequency of the AC source is given by: = 2 = 2 ( 50 ) = 100 rad/s The capacitive reactance X_C is: X_C = 1 C = 1 100 20 10⁻⁶ = 500 The inductive reactance X_L is: X_L = L = 100 1.0 = 100 The impedance Z of the series LCR circuit is: Z = R^2 + (X_C - X_L)^2 = 300^2 + (500 - 100)^2 = 300^2 + 400^2 = 500 The rms current I_ rms in the circuit is: I_ rms = E _ rms Z = 50 500 = 0.1 A The rms potential difference across the capacitor is: V_C = I_ rms X_C = 0.1 500 = 50 V The rms potential difference across th