Question

A fully charged capacitors has a capacitance ${}^{\prime }{C}^{\prime }$. It is discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity $s$ and mass $m$. If the temperature of the block is raised by $\Delta T$, the potential difference $V$ across the capacitor is :

• A. $\sqrt{\frac{2mC\Delta T}{s}}$
• B. $\frac{mC\Delta T}{s}$
• C. $\frac{ms\Delta T}{C}$
• D. $\sqrt{\frac{2ms\Delta T}{C}}$

Answer 1

Answer: (D)

$\sqrt{\frac{2ms\Delta T}{C}}$

By conservation of energy, the stored energy in capacitor will transfer into heat energy during discharging. Thus, $\frac{1}{2}C{V}^2=ms\Delta T\Rightarrow V=\sqrt{\frac{2ms\Delta T}{C}}$