1.

A circuit connected to a 115-V, 50-Hz supply takes 0.8 A at a power factor of 0.3 lagging. Calculate the resistance and inductance of the circuit assuming (a) the circuit consists of a resistance and inductance in series and (b) the circuit consists of a resistance and inductance in paralllel.

Answer»

Z = 115/0.8 = 143.7 Ω ; cos φ = R/Z = 0.3 

∴ R = 0.3 × 143.7 = 43.1Ω

Now XL = √(Z2 - R2) = √(143.72 - 43.12) = 137.1 Ω

∴ L = 137.1/2π × 50 = 0.436 H 

Parallel Combination 

Active component of current (drawn by resistance) 

= 0.8 cos φ = 0.8 × 0.3 = 0.24 A; R = 115/0.24 = 479 Ω 

Quadrature component of current (drawn by inductance) 

= 0.8 sin φ = 0.8√(1 - 0.32) = 0.763A

∴ XL = 115/0.763 Ω 

∴ L = 115/0.763 × 2π × 50 = 0.48 H



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