Calculate Power in Series RCL Circuit

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

Calculate Power in Series RCL Circuit

Figure : Series R-C-L Circuit

Find:

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

Solution:

1. Calculate Z

Z = √R2 + ( XL  –  XC )2

Z = √82 + ( 40  –  24 )2

Z = 17.9Ω

2. Calculate voltage VT

V= I Z

V= 4 x 17.9

V= 71.6 volts

3. Calculate Power factor, p.f.

Calculate Power Factor in Series RCL Circuit

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

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Calculate Power in Series RCL Circuit

 
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