Question

A cardiac defibrillator is used to shock a heart that is beating erratically. A capacitor in this device is charged to 5.0?kVand stores 1600J of energy.

What is its capacitance?

Express your answer using two significant figures and include the appropriate units.

C =

Answer 1

Concepts and reason

The concept required to solve this question is expression of energy stored in a capacitor in terms of capacitance and charge.

Initially, write the expression of energy stored in a capacitor in terms of capacitance and voltage on the capacitor. Rearrange the equation for capacitance. Finally, substitute the values in the equation of capacitance and calculate for capacitance.

Fundamentals

The expression for electric energy (U) stored in a capacitor in terms of capacitance and potential is,

$U = \frac{1}{2}C{V^2}$

Here, V is the voltage on the capacitor and C is the capacitance of the capacitor.

The expression for electric energy (U) stored in a capacitor in terms of capacitance and voltage on the capacitor is,

$U = \frac{1}{2}C{V^2}$

Rearrange the equation $U = \frac{1}{2}C{V^2}$for C.

$C = \frac{{2U}}{{{V^2}}}$

The equation for capacitance in terms of energy and voltage on the capacitor is,

$C = \frac{{2U}}{{{V^2}}}$

Substitute 1600 J for U and 5.0 kV for V.

$\begin{array}{c}\\C = \frac{{2\left( {1600{\rm{ J}}} \right)}}{{{{\left( {5.0{\rm{ kV}}\left( {\frac{{{{10}^3}{\rm{ V}}}}{{1.0{\rm{ kV}}}}} \right)} \right)}^2}}}\\\\ = {\rm{1}}{\rm{.28}} \times {10^{ - 4}}{\rm{ F}}\\\\ = {\rm{1}}{\rm{.3}} \times {10^{ - 4}}{\rm{ F}}\\\end{array}$

Ans:

The capacitance of the capacitor (in two significant figures) is${\rm{1}}{\rm{.3}} \times {10^{ - 4}}{\rm{ F}}$.