An AC generator supplies an rms voltage of 220 V at 50.0 Hz. It is connected in series with a 0.300 H inductor, a 6.00 μF capacitor and a 346 Ω resistor.
What is the impedance of the circuit?

Question

An AC generator supplies an rms voltage of 220 V at 50.0 Hz. It is connected in series with a 0.300 H inductor, a 6.00 μF capacitor and a 346 Ω resistor.
What is the impedance of the circuit?

anonymous · Answer

Please please please help me! :)

anonymous · Answer

since the load is series connected we can simply add the resistance and given reactance... the total impedance $$Z_{TOTAL}=R+j(X_L-X_C)$$
given also is the frequency $f=50$ Hz, we can determine the inductive reactance $$X_L=2 \pi fL=2 \pi (50)(0.30)\approx94.25 ~Ohms$$and capacitive reactance $$X_C=\frac {1}{2 \pi f C}=\frac{1}{2 \pi (50)(6\times10^{-6})}\approx530.52~Ohms$$therefore, the total impedance of the circuit $$Z_{TOTAL}=346+j(94.25-530.52)=346-j436.27~Ohms$$