Question

When two wattmeters are used to measure power of a 3-Φ balanced circuit and one wattmeter reads negative, it means the angle of lag is
1. 0°
2. 30°
3. 60°
4. Above 60°

Answer 1

Correct Answer - Option 4 : Above 60°

Two-wattmeter method:

• If one of the wattmeter shows -ve value then this indicates that the load is a reactive.
• Element i.e. an inductor or a capacitor which consumes the reactive power.
• When p.f. angle = 60°, only single wattmeter measures entire 3-phase power.
• When p.f. angle = 60°, only one wattmeter shows zero deflection.
• When p.f. angle > 60°, one of the wattmeter shown -ve deflection.
• When p.f. angle < 60°, one of the wattmeter shown +ve deflection.
• When one of the wattmeter shows -ve deflection, the range of p.f. is from 0 to 0.5.
• When two wattmeter show +ve deflection, then range of the p.f. is from 0 to 1.

p.f. angle (ϕ)	p.f.(cos ϕ)	W1 [VLTL cos (30 + ϕ)]	W2 [VLTL cos (30 - ϕ)]	W = W1 + W2 [W = √3VLTL cos ϕ]	Observations
0°	1	\(\frac{{\sqrt 3 }}{2}{V_L}{I_L}\)	\(\frac{{\sqrt 3 }}{2}{V_L}{I_L}\)	√3 VLIL	W1 = W2
30°	0.866	\(\frac{{{V_L}I}}{2}\)	VLIL	1.5 VL IL	W2 = 2W1
60°	0.5	0	\(\frac{{\sqrt 3 }}{2}{V_L}{I_L}\)	\(\frac{{\sqrt 3 }}{2}{V_L}{I_L}\)	W1 = 0
90°	0	\(\frac{{ - {V_L}{I_L}}}{2}\)	\(\frac{{{V_L}{I_L}}}{2}\)	0	W1 = -ve W2 = +ve