question_answer

A part of circuit in a steady state along with the currents flowing in the branches, the values of resistances etc., is shown in the figure.   Calculate the energy stored in the capacitor \[C(4.\mu F)\].

A) 0.73 mJ

B) 0.7 mJ

C) 0.8 mJ          

D) 8.0 J

Correct Answer: C

Solution :

[c]:

At steady state, no current flows through capacitor C.

According to Kirchhoff?s law,

(i) at junction \[E,{{I}_{1}}=3A\]

(ii) at junction \[H,{{I}_{2}}=1A\]

(iii) Potential difference across capacitor,

Or

\[V=(6\times 3)+(2\times 1)=18+2=20V\]

\[\therefore \]Energy \[=\frac{1}{2}C{{V}^{2}}\]

Or

\[U=\frac{1}{2}\times (4\times {{10}^{-6}})\times {{(20)}^{2}}=8\times {{10}^{-4}}J\]