The rms voltages across the components of a series LCR circuit are given below: Resistor ( R ): 16 V Inductor ( L ): 24 V Capacitor ( C ): 12 V The instantaneous current flowing through the circuit is given by the equation i(t) = 4 2 (100 t) A . The impedance of the circuit is:

Step-by-step solution

The rms voltage of the source is calculated using the phasor addition formula: V_ rms = V_R^2 + (V_L - V_C)^2 V_ rms = 16^2 + (24 - 12)^2 = 256 + 144 = 400 = 20 V The peak current from the given equation i(t) = 4 2 (100 t) is I₀ = 4 2 A . The rms current is: I_ rms = I₀ 2 = 4 2 2 = 4 A The impedance of the circuit is: Z = V_ rms I_ rms = 20 4 = 5 Answer: 5