Question

A three pahse 400-V, 50 Hz, a.c. supply is feeding a three phase delta connected load with each phase having a resistance of 25 ohms, an inductance of 0.15 H, and a capacitor of 120 micro farads in series. Determine the line current, volt-amp, active power and reactive volt-amp.

Answer 1

Impedance per phase r + jX_L – jX_C

X_L = 2π x  50 x 0.15 = 47.1Ω

X_C = 10⁶/32.37 = 26.54Ω

cosφ = 25/32.37

Lagging, since inductive reactance is dominating.

Phase Current = 400/(25 + j20.56) = 12.357

Line Current = √3 x 12.357 = 21.4amp

Since the power factor is 0.772 lagging,

P = total three phase power = √3V_LI_L cosφ x 10^-3KW

= √3 x 400 x 21.4 x 0.772 x 10^-3 = 11.446KW

S = total 3 ph KVA 11.446/0.772 = 14.83KVA

Q = total 3 ph “reactive kilo-volt-amp”

√3 = (S² - P²)0.50 = 9.43 kVAR lagging