Question

In a 3-$\phi$ star connected balanced circuit, if angle between phase voltage \( V_p \) and phase current is \( \theta \) (leading), then the wattmeter readings in two wattmeter method are:

• A. \( \sqrt{3} V_p I_p \cos(30^\circ + \theta) \) and \( \sqrt{3} V_p I_p \cos(60^\circ - \theta) \)
• B. \( 3 V_p I_p \cos(30^\circ + \theta) \) and \( 3 V_p I_p \cos(60^\circ - \theta) \)
• C. \( V_p I_p \cos(30^\circ + \theta) \) and \( V_p I_p \cos(30^\circ - \theta) \)
• D. \( \sqrt{3} V_p I_p \cos(30^\circ + \theta) \) and \( \sqrt{3} V_p I_p \cos(30^\circ - \theta) \)

Hint:

Remember — in a star connected system, the two wattmeter readings depend on \( \theta \) and involve \( \cos(30^\circ \pm \theta) \).

Answer 1

The Correct Option is D

In a balanced 3-phase star connected circuit, the two wattmeter method is commonly used to measure the total power. This method provides readings of two wattmeters, W1 and W2, which can be derived by considering the phase voltage \( V_p \) and the phase current \( I_p \) with an angle \( \theta \) between them (leading).

The readings of the two wattmeters in the two-wattmeter method are given by:

\( W1 = V_p I_p \cos(30^\circ + \theta) \)

\( W2 = V_p I_p \cos(30^\circ - \theta) \)

When we convert these into line values, using \( V_L = \sqrt{3}V_p \), the expressions become:

\( W1 = \sqrt{3}V_p I_p \cos(30^\circ + \theta) \)

\( W2 = \sqrt{3}V_p I_p \cos(30^\circ - \theta) \)

Therefore, the correct formula for the wattmeter readings are: \( \sqrt{3} V_p I_p \cos(30^\circ + \theta) \) and \( \sqrt{3} V_p I_p \cos(30^\circ - \theta) \).