Question

An a.c. source of 200 V rms supplies active power of 600 W and reactive power of 800 VAR. The rms current drawn from the source is ____.

• A. 10 A
• B. 5 A
• C. 3.75 A
• D. 2.5 A

Hint:

The values 600, 800, and 1000 form a 6:8:10 (or 3:4:5) Pythagorean triple. Recognizing these triples allows you to find the hypotenuse (Apparent Power) instantly without doing long calculations.

Answer 1

The Correct Option is B

Step 1: Find the power factor angle from the given active and reactive powers: \[ \phi = \arctan\left(\frac{Q}{P}\right) = \arctan\left(\frac{800}{600}\right) \approx 53.13^\circ \]

Step 2: Use \( \cos\phi = \dfrac{P}{S} \) to find the apparent power: \[ S = \frac{P}{\cos\phi} = \frac{600}{\cos 53.13^\circ} = \frac{600}{0.6} = 1000 \text{ VA} \]

Step 3: Divide the apparent power by the rms voltage to get the rms current: \[ I_{rms} = \frac{S}{V_{rms}} = \frac{1000}{200} = 5 \text{ A} \] \[ \boxed{I_{rms} = 5 \text{ A}} \]