Two capacitors, each of capacitance \(\frac{50}{\pi}\ \mu\mathrm{F}\), are connected in parallel across a 220 V, 50 Hz ac supply. The rms current drawn from the supply is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 2.2 A
Capacitances joined in parallel add up. The combination then acts as one capacitor of reactance \( X_C=1/\omega C \), and the rms current is \( I=V/X_C \).
Given:
\( V=220\ \mathrm{V} \)
\( \nu=50\ \mathrm{Hz} \)
\( \begin{aligned} C &= C_1+C_2 \\ &= \frac{50}{\pi}+\frac{50}{\pi} \\ &= \frac{100}{\pi}\ \mu\mathrm{F} \end{aligned} \)
\( \begin{aligned} X_C &= \frac{1}{2\pi\nu C} \\ &= \frac{1}{2\pi\times50\times\frac{100}{\pi}\times10^{-6}} \\ &= \frac{1}{10^{-2}} \\ &= 100\ \Omega \end{aligned} \)
\( \begin{aligned} I &= \frac{V}{X_C} \\ &= \frac{220}{100} \\ &= 2.2\ \mathrm{A} \end{aligned} \)
NCERT (2026-27):
AC Voltage Applied to a Capacitor – “Comparing it to im = vm/R for a purely resistive circuit, we find that (1/ωC) plays the role of resistance. It is called capacitive reactance and is denoted by Xc,”
\( X_c=1/\omega C \)\( \qquad (7.17) \)
“so that the amplitude of the current is”
\( i_m=\frac{v_m}{X_C} \)\( \qquad (7.18) \)
Capacitors in parallel – “… The effective capacitance C is …”
\( C=C_1+C_2 \)\( \qquad (2.64) \)