A fully charged capacitor has a capacitance C. It is discharged through a small coil of resistance…

Q: 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  ΔT, the potential difference V across the capacitor is

(a) $ \displaystyle \sqrt{\frac{2 m C \Delta T}{S} }$

(b) $ \displaystyle \frac{ m C \Delta T}{S} $

(c) $ \displaystyle \frac{ m S \Delta T}{C} $

(d) $ \displaystyle \sqrt{\frac{2 m S \Delta T}{C}} $

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Ans: (d)
Sol: $ \displaystyle \frac{1}{2}C V^2 = m S \Delta T$

$ \displaystyle V = \sqrt{\frac{2 m S \Delta T}{C}} $