A resistor and a capacitor are connected in series with an alternating current source. The potential difference across resistor and capacitor are 90 V and 120 V respectively and rms value of current is 3 A. What is the power factor of the circuit?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 0.6
In a series RC circuit the voltage across R is in phase with the current and the voltage across C lags it by \( 90^\circ \), so the two add as perpendicular phasors. The power factor is \( \cos\phi = R/Z = V_R/V \).
\( V = \sqrt{V_R^{2} + V_C^{2}} = \sqrt{90^{2} + 120^{2}} = 150\,\mathrm{V} \)
\( \displaystyle \cos\phi = \frac{V_R}{V} = \frac{90}{150} = 0.6 \)
The current of 3 A is not needed: it gives \( R = 30\,\Omega \) and \( Z = 50\,\Omega \), the same ratio.