Example 19.11 from College Physics, 19.7 Energy Stored in Capacitors

Capacitance in a Heart Defibrillator

A heart defibrillator delivers $4.00 \times 10^{2} J$ of energy by discharging a capacitor initially at $1.00 \times 10^{4} V$ . What is its capacitance?

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
We are given $E_{cap}$ and $V$ , and we are asked to find the capacitance $C$ . Of the three expressions in the equation for $E_{cap}$ , the most convenient relationship is
$E_{cap} = \frac{{CV}^{2}}{2} .$
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Solution
Solving this expression for $C$ and entering the given values yields
$\begin{array}{l} C & = & \frac{2 E_{cap}}{V^{2}} = \frac{2 (4.00 \times 10^{2} J)}{(1.00 \times 10^{4} V)^{2}} = 8.00 \times 10^{- 6} F \\ = & 8 . 00 µF . \end{array}$
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Discussion
This is a fairly large, but manageable, capacitance at $1.00 \times 10^{4} V$ .

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