Power in Series R-C Circuit:

Example:  An 80? Xc and a 60? resistance are in  series  with  a 120V source, as shown in Figure.

Find:  

1. Z

2. I_T

3. pf

4. P

5. Q

6. S

Figure  Series R-C Circuit

Solution:

1.Z = √R² + X²_C

= √60²  + 80²

= √3600 + 6400

Z =100?

2. I_T =V_T/Z

=    120/ 100

I_T  = 1.2 amps

3. pf= cosθ            θ -arctan(-X_C/R)

= cos(arctan(-X_C/R))

= cos(arctan(-80 /60))

= cos(arctan (-1.33))

= cos(-53º)

pf= 0.60

4. P =  EI cosθ

= (120)(1.2)(0.60)

P = 86.4 watts

5. Q = EI sinθ

= (120)(1.2)(0.798)

Q = 114.9 VAR

6. S = EI

(120)(1.2)

S= 144 VA