Question

A fully charged capacitor has a capacitance $C$. It is discharged through a small coil of resistance wire, embedded in a block of specific heat $s$ and mass $m$ under thermally isolated conditions. If the temperature of the block is raised by $\Delta T$, the potential difference $V$ across the capacitor initially is:

• A. ${\left(\frac{2ms\Delta T}{C}\right)}^2$
• B. ${\left(\frac{2ms\Delta T}{C}\right)}^{1/2}$
• C. $\left(\frac{2ms\Delta T}{C}\right)$
• D. $2ms\Delta TC$

Answer 1

Answer: (B)

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

Given that temperature of the block is raised by $\Delta T$.

The heat gained by the block is, $Q=ms\Delta T$

Also energy stored in the capacitor is given by: $E=\frac{1}{2}C{V}^2$

$\Rightarrow$$\frac{1}{2}C{V}^2=$$ms\Delta T$

$\Rightarrow V=\sqrt{\frac{2ms\Delta T}{C}}$