Calculate Power in Series RC Circuit

An 80 Ω X_C and a 60 Ω resistance are in series with a 120V source, as shown in Figure.

Figure : Series R-C Circuit

Find:

1. Z
2. Current, I_T
3. Power Factor, pf
4. True Power, P
5. Reactive Power, Q
6. Apparent Power, S

Solution : 

1. Calculate Z

Z = √R² + X_C²

Z = √60² + 80²

Z = 100 Ω

2.Current, I_T

I_T = V_T/Z

I_T = 120/100

I_T = 1.2 amps

2. Calculate Power factor (pf)

p.f. = cos (- 53º)

p.f. = 0.6

3. Calculate True Power, P

P = EI cos θ

P = (120)(1.2)(0.6)

P = 86.4 watts

4. Calculate Reactive Power, Q

Q = EI sin θ

Q = (120)(1.2)(0.798)

Q = 114.9 VAR

5. Calculate Apparent Power, S

S = EI

S = (120)(1.2)

S = 144 VA