JEE Main · 2005 · 08 May 2005 · Offline · Capacitance

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 '

Δ T

'. The potential difference V across the capacitance is

(A) $\frac{2 m C Δ T}{s}$
(B) $\frac{m C Δ T}{s}$
(C) $\frac{m s Δ T}{C}$
(D) $\frac{2 m s Δ T}{C}$ ✓ Correct

Answer: (D)

Solution

All the capacitor's stored energy

\frac{1}{2} C V^{2}

ends up heating the block,

\frac{1}{2} C V^{2} = m s Δ T

. Solving for the voltage,

V^{2} = \frac{2 m s Δ T}{C}

, so

V = \frac{2 m s Δ T}{C}

JEE Main · 2005 · 08 May 2005 · Offline · Single correct option

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