Question

Calculate the steadystate current in the $2\,\Omega$ resistor shown in the circuit in the figure. The internal resistance of the battery is negligible and the capacitance of the condenser $C$ is $0.2\, \mu F$.

• A. $0.6\,A$
• B. $0.9\,A$
• C. $1.2\,A$
• D. $0.1\,A$

Answer 1

Answer: (B)

$0.9\,A$

Answer 2

At steady state, no current flows through the capacitor branch of the circuit. $2\,\Omega$ and $3\,\Omega$ are in parallel. Let their combined resistance be $R$. $\therefore R=\frac{2 \times 3}{2+3}=\frac{2\times3}{5}$ $=1.2\,\Omega$ Net current supplied $=\frac{6}{1.2+2.8}$ $I=1.5\,A$ $I$ divides into $I_{1}$ and $I_{2}$ $2I_{1}=3I_{2}\quad$ [Potential Difference is same] or $I_2=2I_1/3$ $I_{1}+I_{2}=1.5$ or $I_{1}+\frac{2I_{1}}{3}$ $=1.5$ or $\frac{5I_{1}}{3}=1.5$ or $I_{1}=\frac{1.5 \times 3}{5}\,A$ $=0.9\,A$