Answer to Question #166859 in Material Science Engineering for KEERTHANA UNNIKRISHNAN E

Question

Two impedances Z1 and Z2 are connected in parallel. The first branch takes a leading current of 16 A and has a resistance of 5 Ω, while the second branch takes a lagging current at 0.8pf. The applied voltage is 100+j200 V and the total power is 5 kW. Find branch impedances, total circuit impedance, branch currents and total circuit current.

Answer 1

I₁ = 16 0°

V = 100 + j200

P = 5 kW

P = P₁ + P₂ = I₁²R₁ + I₂²R₂

5000 W = 16² x 5 + I₂²R₂

I₂²R₂ = 3720 W

p.f. = cos $\phi$ = 0.8

$\phi$ = 37°

Z₁ = V/I₁ = (100 + j200) / 16 0°

Z = Z₁ + Z₂