A cardiac defibrillator can be used to help an erratic heartbeat in a regular fashion.A defibrillator contains a capacitor charged to a voltage of 6000 V with an energy storage of 200 J.Calculate the capacitance of the capacitor. A)6.67 $\times$ 10^-2 F B)1.11 $\times$ 10^-5 F C)5.56 $\times$ 10^-6 F D)2.22 $\times$ 10^-5 F E)13.3 F

Question

Quizplus · Accepted Answer

The capacitance $C$ of a capacitor can be calculated using the formula for stored energy in a capacitor, $E = \frac{1}{2}CV^2$, where $E$ is the energy in joules, $C$ is the capacitance in farads, and $V$ is the voltage in volts. Rearranging the formula to solve for $C$ gives $C = \frac{2E}{V^2}$. Substituting $E = 200 \, \text{J}$ and $V = 6000 \, \text{V}$ into the formula gives $C = \frac{2 \times 200}{6000^2} = \frac{400}{36 \times 10^6} = \frac{1}{90 \times 10^3} = 1.11 \times 10^{-5} \, \text{F} = 11.1 \, \mu\text{F}$, which corresponds to choice B when expressed in scientific notation as $1.11 \times 10^{-5} \, \text{F}$.

A Cardiac Defibrillator Can Be Used to Help an Erratic ×\times×

A Cardiac Defibrillator Can Be Used to Help an Erratic $\times$