To an AC power supply of 150 V (rms), a resistor of $40 \Omega$, a capacitor of reactance $40 \Omega

Question

To an AC power supply of 150 V (rms), a resistor of $40 \Omega$, a capacitor of reactance $40 \Omega$, and an inductor of reactance $70 \Omega$ are connected in series. The corresponding rms current in the circuit and the phase angle between the current and the voltage are, respectively

Professor PC Thomas Classes · Answer

(b) : Given $V_{rms} = 150$ V, $R = 40 \Omega$, $X_L = 70 \Omega$, and $X_C = 40 \Omega$. The net reactance is $X = X_L - X_C = 70 - 40 = 30 \Omega$. The impedance of the circuit is $Z = \sqrt{R^2 + X^2} = \sqrt{40^2 + 30^2} = 50 \Omega$. The rms current is $I_{rms} = V_{rms} / Z = 150 / 50 = 3$ A. The phase angle is $\phi = 	an^{-1}(X/R) = 	an^{-1}(30/40) = 	an^{-1}(3/4)$.