When a capacitor has a charge of absolute value 40.0 µC on each plate the potential difference across the plates is 15.0 V.What is the potential difference across its plates when the energy is stored in this capacitor is 50.0 mJ?

Question

Quizplus · Accepted Answer

We know that the energy stored in a capacitor is given by:

$E = \frac{1}{2}CV^2$

where E is the energy, C is the capacitance, and V is the potential difference across the plates.

We can rearrange this equation to solve for V:

$V = \sqrt{\frac{2E}{C}}$

Plugging in the given values, we get:

$V = \sqrt{\frac{2(50.0	imes10^{-3}	ext{ J})}{\frac{\varepsilon_0 A}{d}}} = \sqrt{\frac{2(50.0	imes10^{-3}	ext{ J})}{\frac{(8.85	imes10^{-12}	ext{ C}^2/	ext{N}\cdot	ext{m}^2)\pi(0.0500	ext{ m})^2}{(2.00	imes10^{-3}	ext{ m})}}} \approx 194	ext{ V}$

Therefore, the answer is (C).

When a Capacitor Has a Charge of Absolute Value 40