The diagram below illustrates an a.c.source of 50V(r.m.s.), \(\frac{100}{\pi}\)Hz connected in series with an inductor of inductor of inductance L and a resistor of resistance R. The current in the circuit is 2A and the p.d across L and R are 30V and 40V respectively. Calculate the power factor of the circuit
Attached Figure / Diagram
A
1.33
B
1.25
C
0.80
D
0.75
E
0.60
Verified Correct Answer: C.
Physical Principles & Numerical Solution
cos\(\theta = \frac{R}{Z}\)
R = \(\frac{V}{I} = \frac{40}{2} = 20\)
Z² = R² + \(^X_L\)² = 20² + 15² = \sqrt625 = 25
cos \(\theta = \frac{R}{Z} = \frac{20}{25} = 0.8\)
Source: Myschool Past Questions Archive (Record #33690)