Question

The inductive reactance of the pressure-coil circuit of a dynamometer watt meter is 0.4 % of its resistance at normal frequency and the capacitance is negligible. Calculate the percentage error and correction factor due to reactance for load at (i) 0.707 p.f. lagging and (ii) 0.5 p.f. lagging.

Answer 1

It is given that Xp/R = 0.4 R = 0.004

tan α = Xp/R = 0.004

∴ α = 0 14′ and sin α = 0.004

(i) When p.f. = 0.707 (i.e. φ = 45)

Correction factor = cosφ/cos(φ + α) = cos 45/(cos 4446) = 0.996

Percentage error = sinα/(cotφ + sinα) x 100 = (sin 0 14')/(cot 45 sin 0 14') x 100

= (0.004 x 100)/(1 + 0.004) = 0.4/1.004 = 0.4(approx)

(ii) when p.f. = 0.5(i.e., φ = 60)

Correction factor = cos60/cos5946 = 0.993

Percentage error = sin 0 14/(cot60 + sin014) x 100

= (0.004 x 100)/(0.577 + 0.004) = 0.4/0.581 = 0.7