Question

A fully charged capacitor has a capacitance '$C$'. 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 ${}^{\prime }\Delta T^{\prime }$, the potential difference '$V$' across the capacitance is :

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

Answer 1

The correct option is C $\sqrt{\frac{2ms\Delta T}{C}}$

Energy stored in the capacitor is $U=\frac{1}{2}C{V}^2$ and
Heat energy in the wire is $H=ms.\Delta T$
According to conservation of energy, the stored energy in the capacitor will be converted into heat energy.
So, $U=H$
$\frac{1}{2}C{V}^2=ms.\Delta T$
$\therefore V=\sqrt{\frac{2ms.\Delta T}{C}}$