In the circuit shown, an alternating voltage source is connected to a resistor, an inductor, and a capacitor in series. The readings of the ideal voltmeters V₁ , V₂ , and V₃ connected across the resistor, inductor, and capacitor are 16 V , 24 V , and 12 V respectively. If the amplitude of the current in the circuit is 2 2 A , what is the impedance of the circuit?

Step-by-step solution

The readings of the AC voltmeters give the RMS voltage across the respective components. V_R = 16 V V_L = 24 V V_C = 12 V The total RMS voltage of the source is: V_ rms = V_R^2 + (V_L - V_C)^2 V_ rms = 16^2 + (24 - 12)^2 = 16^2 + 12^2 = 20 V The amplitude of the current is I₀ = 2 2 A . The RMS current is: I_ rms = I₀ 2 = 2 2 2 = 2 A The impedance of the circuit is: Z = V_ rms I_ rms = 20 2 = 10 Answer: 10