In a short transmission line, the reactance and resistance are equal. Find the characteristics of the load, if the voltage regulation is zero.

The correct answer is option 1): (0.707 leading)

Concept:

• In a short transmission line, the length of the line is below 80 km, and the line voltage is comparatively low (below 69 kV). Hence the capacitance effects of the line are extremely small and thus neglected.
• Voltage regulation = \(= \frac{{IRcos{\phi _r} \pm IXsin{\phi _r}}}{{{V_r}}} \times 100\;\)

For zero voltage regulation,

IV(Rcos⁡ϕ−Xsin⁡ϕ) = 0 (leading power factor)

⇒ tan ϕ = \( R\over X\) If R = X,

then tan ϕ = 1 ⇒ ϕ = 45°

Power factor, cos ϕ = cos 45°= 0.707 leading power factor​