Power Factor- Parallel Circuits

Determine R and X

given V, I and P

V is found from a Voltmeter

I is found from an ammeter

P is found from a wattmeter

Definitions

• G = (1/R) is called conductance

• B = (1/X) is called sucepatance

• BL (for an inductor) = (1/jL) = (-j/L)

• BC (for a capacitor) = (1/(1/jC)) = jC

• Y = (1/Z) is called admittance

• For a parallel RL circuit:

• Y = G - jBL

Example # 2

• Given:

• The voltmeter reading is 120 volts

• The ammeter reading 15 amps

• The wattmeter reading is 900 watts

• Determine:

1. R

2. jXL

Solution

• Solve for • = cos-1(P/VI) = cos-1(900/(120x15)) = 60o

• Y = (I/V) / - = (15/120) / - 0.125/ -60o

• This is in Polar form - and• Y= 0.0625 - j 0.10825 (in Rectangular form)• We now have:• G = 0.0625 S

• jBL = -j 0.10825 S

To find R

• G = 0.0625 S• But we don’t want G we want R• To find R:1. Program your calculator for Complex

operations (CPLX)2. Press “real” (F2) (0.125/-60o)3. Now invert the answer to find

R = 16

To Find X

• B = 0.1082 S• But we don’t want B we want X• To find X:1.Program your calculator for Complex

operations (CPLX)2.Press “imag” (F3) (0.125/-60o) 3.Now invert the answer to find

jXL = j9.237