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Power Factor- Parallel Circuits

This guide details how to determine resistance (R) and reactance (X) in parallel circuits using voltmeter, ammeter, and wattmeter readings. Definitions of key terms such as conductance, susceptance, and admittance are provided. An example illustrates the process: with a voltmeter reading of 120V, an ammeter reading of 15A, and a wattmeter reading of 900W, calculations reveal values of resistance and reactance. Step-by-step instructions for using complex operations on a calculator are included to simplify the calculations.

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Power Factor- Parallel Circuits

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  1. 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

  2. Definitions • G = (1/R) is called conductance • B = (1/X) is called sucepatance • BL (for an inductor) = (1/jwL) = (-j/wL) • BC (for a capacitor) = (1/(1/jwC)) = jwC • Y = (1/Z) is called admittance • For a parallel RL circuit: • Y = G - jBL

  3. Example # 2 • Given: • The voltmeter reading is 120 volts • The ammeter reading 15 amps • The wattmeter reading is 900 watts • Determine: • R • jXL

  4. Solution • Solve for q • q = cos-1(P/VI) = cos-1(900/(120x15)) = 60o • Y = (I/V) / -q = (15/120) / -q = 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

  5. To find R • G = 0.0625 S • But we don’t want G we want R • To find R: • Program your calculator for Complex operations (CPLX) • Press “real” (F2) (0.125/-60o) • Now invert the answer to find R = 16 W

  6. To Find X • B = 0.1082 S • But we don’t want B we want X • To find X: • Program your calculator for Complex operations (CPLX) • Press “imag” (F3) (0.125/-60o) • Now invert the answer to find jXL = j9.237 W

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