Question

A fully charged capacitors 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 capacitor is :

A
2mCΔTs
B
mCΔTs
C
msΔTC
D
2msΔTC

Solution

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

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