A resistor of 300 Ω and a capacitor of \( \displaystyle\frac{25}{\pi} \) μF are connected in series to a 220 V, 50 Hz ac source. The rms value of the current in the circuit is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 0.44 A
In a series RC circuit the resistance and the capacitive reactance combine into the impedance as the sides of a right-angled triangle, because the voltages across them are 90° out of phase. The 220 V of an ac supply is its rms value.
\( \displaystyle X_C = \frac{1}{2\pi f C} \)
\( \displaystyle X_C = \frac{1}{2\pi \times 50\,\mathrm{Hz} \times \frac{25}{\pi}\times10^{-6}\,\mathrm{F}} \)
\( \displaystyle X_C = \frac{1}{2500\times10^{-6}}\,\Omega = 400\,\Omega \)
\( \displaystyle Z = \sqrt{R^{2} + X_C^{2}} = \sqrt{300^{2} + 400^{2}}\,\Omega \)
\( Z = 500\,\Omega \)
\( \displaystyle I_{\mathrm{rms}} = \frac{V_{\mathrm{rms}}}{Z} = \frac{220\,\mathrm{V}}{500\,\Omega} \)
\( I_{\mathrm{rms}} = 0.44\,\mathrm{A} \)