A fully charged capacitor has a capacitance C | vedclass

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Question

(B) Let $V$ be the potential difference across the capacitor when it is fully charged. The energy stored in the capacitor is given by $U = \frac{1}{2}

Vedclass · Accepted Answer

$\left(\frac{2 m s \Delta T}{C}\right)^{1 / 2}$

Vedclass · Answer

(B) Let $V$ be the potential difference across the capacitor when it is fully charged. The energy stored in the capacitor is given by $U = \frac{1}{2} C V^2$.When the capacitor is fully discharged through the resistance wire,the entire stored energy is dissipated as heat $\Delta H$ in the block.Since the system is thermally isolated,the heat gained by the block is equal to the energy lost by the capacitor: $\Delta H = U = \frac{1}{2} C V^2$.The heat gained by the block is also given by the formula $\Delta H = m s \Delta T$,where $m$ is the mass,$s$ is the specific heat,and $\Delta T$ is the rise in temperature.Equating the two expressions for $\Delta H$: $\frac{1}{2} C V^2 = m s \Delta T$.Solving for $V$: $V^2 = \frac{2 m s \Delta T}{C}$,which gives $V = \left(\frac{2 m s \Delta T}{C}\right)^{1 / 2}$.

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