First slide

Capacitance

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 $∆ T$ , the potential difference V across the capacitance is

Moderate

A

$\sqrt{\frac{2 mC ∆ T}{s}}$
B

$\frac{mC ∆ T}{s}$
C

$\frac{ms ∆ T}{C}$
D

$\sqrt{\frac{2 ms ∆ T}{C}}$

Solution

$\begin{array}{rcl} U & = & \frac{1}{2} {CV}^{2} = ms ∆ T \\ V^{2} & = & \frac{2 ms ∆ T}{C} \\ \Rightarrow & V = \sqrt{\frac{2 ms ∆ T}{C}} \end{array}$

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