Question

The figure shows a network of capacitor and resistances. Potentials of some of the points are given. The energy ($U$) stored in the capacitor at steady state and the rate of heat dissipated $\left(H\right)$ in $1\Omega$ resistor at steady state are:

• A. $U=4\mu J$
• B. $U=8\mu J$
• C. $H=8\mu W$
• D. $H=1W$

Answer 1

Answer: (A), (D)

The correct options are
A $U=4\mu J$
D $H=1W$

Here in steady state, no current flows through the capacitor branch.

And current in $1\Omega$ and $2\Omega$ resistance are same.

And is $=\frac{3}{3}=1A$

Rate of heat dissipation$=i^{2}R=1^2\times 1=1W$

And potential difference accross the capacitor$=2V$

$U=\frac{1}{2}C{V}^2=\frac{1}{2}\times 2\times 2^2=4\mu J$

Option $\text{A,D}$ is the correct answer.