Question

The circuit shown has been connected for a long time. The voltage across the capacitor is :

• A. 6 V
• B. 2.0 V
• C. 2.4 V
• D. 4.0 V

Answer 1

The correct option is A 6 V

Let the current be divided as $I_1$ $=$ $I_2+I_3$

As the circuit is connected for a long time, the current through the capacitor is 0. Thus the 1$\Omega$ and 4$\Omega$ resistance is in series. Also, the 2$\Omega$ and 8$\Omega$ resistance is in series.

Using Kirchoff's laws, when we solve the resistances in series, we get

$I_2$ $=$ 10V/5$\Omega$ $=$ 2A

$I_3$ $=$ (1$\Omega$ $I_2$ +$V_2$) /8$\Omega$

Solving the above two equations, the voltage across the capacitor is given as:

$V_c$ $=$ $I_2$3$\Omega$

or $V_c$ is 6V.