Calculate Power in Series RCL Circuit

An 8 Ω resistance, a 40 Ω X_L, and a 24 Ω X_C are in series with a 60 Hz source with a current flow of 4 amps, as shown in Figure.

Figure : Series R-C-L Circuit

Find:

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

Solution:

1. Calculate Z

Z = √R² + ( X_L  –  X_C )²

Z = √8² + ( 40  –  24 )²

Z = 17.9Ω

2. Calculate voltage V_T

V_T = I Z

V_T = 4 x 17.9

V_T = 71.6 volts

3. Calculate Power factor, p.f.

p.f. = cos (63.4º)

p.f. = 0.45

4. Calculate True Power, P

P = EI cos θ

P = (71.6)(4)(0.45)

P = 128.9 watts

5. Calculate Reactive Power, Q

Q = EI sin θ

Q = (71.6)(4)(0.89)

Q = 254.9 VAR

6. Calculate Apparent Power, S

S = EI

S = (71.6)(4)

S = 286.4 VA