Question

The power in a 400 V (rms, line-line) three-phase, three-wire RYB sequence system is measured using the two wattmeters, as shown. The R-line current is \( 5 \angle 60^\circ \, \text{A} \). Wattmeter \( W_1 \) in the R-line will read (in watts) \(\underline{\hspace{2cm}}\). 

Hint:

To calculate the power in a three-phase system, use the wattmeter formula \( W = V_L I_L \cos(\theta) \), where \( \theta \) is the phase angle of the current.

Answer 1

Correct Answer: 0

In a three-phase system, the readings of the two wattmeters \( W_1 \) and \( W_2 \) can be used to determine the total power. The power measured by \( W_1 \) is given by: \[ W_1 = V_L I_L \cos(\theta_1) \] where \( V_L = 400 \, \text{V} \) (line-line voltage), \( I_L = 5 \, \text{A} \) (line current), and \( \theta_1 = 60^\circ \). Substituting the values: \[ W_1 = 400 \times 5 \times \cos(60^\circ) = 400 \times 5 \times \frac{1}{2} = 1000 \, \text{W}. \] Thus, the reading of \( W_1 \) is \( 1000 \, \text{W} \).