Question

A parallel plate capacitor of capacitance $C$ is connected to a battery and is charged to a potential difference $V$. Another capacitor of capacitance $2C$ is similarly charged to a potential difference $2V$. The charging battery is now disconnected, and the capacitors are connected in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. Find heat dissipated in the system ?

• A. Zero
• B. $3C{V}^2$
• C. $\frac{5}{2}C{V}^2$
• D. $\frac{9}{2}C{V}^2$

Answer 1

The correct option is B $3C{V}^2$

$\text{Heat dissipated,}H=U_i-U_f$

$\Rightarrow H=\frac{1}{2}{C}_1{V}_1^2+\frac{1}{2}{C}_2{V}_2^2-\frac{1}{2}{C}_{eq}{(V_2-V_1)}^2$

$=\frac{1}{2}C{V}^2+4C{V}^2-\frac{1}{2}\times 3C{V}^2$

$=3C{V}^2$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(B\right)$ is the correct answer.