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 by $\Delta T$, the potential difference $V$ across the capacitance is:

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

Answer 1

Answer: (C)

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

Answer 2

$E=\left(\frac{1}{2}\right)CV^{2}\,...\left(i\right)$ The energy stored in capacitor is lost in form of heat energy. $H=ms\,\Delta T\,...\left(ii\right)$ From Eqs. $\left(i\right)$ and $\left(ii\right)$, we have $ms\,\Delta T=\left(\frac{1}{2}\right)CV^{2}$ $V=\sqrt{\frac{2ms\Delta T}{C}}$