Question

3. 21 A three-phase load draws 120 kW at a power factor of 0. 85 lagging from a 40-V bus. In parallel with this load is a three-phase capacitor bank that is rated 50 VAR. Find (a) the total line current and (b) the resultant power factor

Answer 1

To calculate the total line current, we can use the formula:

I = P / (sqrt(3) x V x pf)

where I is the line current, P is the power, V is the voltage, and pf is the power factor.

Substituting the given values, we get:

I = 120,000 / (sqrt(3) x 40 x 0.85) = 1,389 A

To find the resultant power factor, we can use the formula:

pf = (P1 + P2) / (sqrt(3) x V x I)

where P1 is the power of the load, P2 is the reactive power of the capacitor bank, and the rest of the variables are as defined above.

Substituting the given values, we get:

pf = (120,000 + 50) / (sqrt(3) x 40 x 1,389) = 0.872 lagging

Therefore, the total line current is 1,389 A and the resultant power factor is 0.872 lagging.