Alternating Current SQP 2018

Question

An 8H inductor, a 2μF capacitor and a 100 Ω resistor are connected in series to an A.C. supply of 220 V and 50 Hz. Calculate:

(i) Impedance of the circuit

(ii) Current flowing through the circuit

(iii) Phase difference between the current and the supply voltage

(iv) Average power consumed by the circuit

Answer 1

(i) Impedance of the circuit

\(Ƶ=\sqrt{R^2+(X_L-X_c)^2}\)

\(Ƶ=\sqrt{(100)^2+(2512-1592)^2}\)

\(Ƶ=\sqrt{(100)^2+(920)^2}\)

\(Ƶ=\sqrt{1000+846400}\)

\(Ƶ=\sqrt{856400}\)

Ƶ = 925.4Ω

(ii) Current flowing through the circuit

\(i=\frac{v}{7}\)

\(i=\frac{220}{925.4}\)

i = 0.237 A

(iii) Phase difference between the current

\(Φ=tan^{-1}(\frac{X_L-X_C}{R})\)

\(Φ=tan^{-1}(\frac{920}{100})\)

\(Φ=83.7°\)

(iv) P_avg = i²R

P_avg = (0.237)² x 100

P_avg = 5.6 watt