If you want to store $2.0 \mathrm {~mJ}$ of energy in a $10 - \mu \mathrm { F }$ capacitor, how much potential do you need to put across it?

Question

Quizplus · Accepted Answer

The energy stored in a capacitor is given by the formula $E = \frac{1}{2} C V^2$, where $E$ is the energy in joules, $C$ is the capacitance in farads, and $V$ is the potential difference in volts. Rearranging the formula to solve for $V$, we get $V = \sqrt{\frac{2E}{C}}$. Substituting $E = 2.0 \times 10^{-3}$ J (since $1 \mathrm{mJ} = 10^{-3} \mathrm{J}$) and $C = 10 \times 10^{-6}$ F (since $1 \mu \mathrm{F} = 10^{-6} \mathrm{F}$), we find $V = \sqrt{\frac{2 \times 2.0 \times 10^{-3}}{10 \times 10^{-6}}} = \sqrt{400} = 20$ V.

If You Want to Store 2.0 mJ2.0 \mathrm {~mJ}2.0 mJ Of Energy in A

If You Want to Store $2.0 \mathrm {~mJ}$ Of Energy in A