Question

The energy stored in a capacitor of capacity C and potential V is given by

• A. $ \frac{ CV}{ 2}$
• B. $ \frac{ C^2 V^2 }{ 2} $
• C. $ \frac{ C^2V}{ 2}$
• D. $ \frac{ CV^2}{ 2}$

Answer 1

The Correct Option is D

To determine the energy stored in a capacitor, we use the formula for the energy stored in a capacitor, which is derived from the basic principles of capacitance and electric potential energy.

1. For a capacitor with capacitance C and potential difference V across its plates, the energy stored U is given by: U = \frac{1}{2} C V^2
2. Let's break down the terms:
   • C is the capacitance of the capacitor, which is a measure of its ability to store charge per unit voltage.
   • V is the potential difference across the capacitor.
   • The factor \frac{1}{2} comes from the integration of the voltage charge relation over the interval of 0 to V.
3. Substituting into the formula, we get: U = \frac{1}{2} C V^2, which matches the correct answer given as \frac{CV^2}{2}.
4. Comparing the options:
   • \frac{CV}{2}: Incorrect, as it does not account for the square of voltage.
   • \frac{C^2 V^2}{2}: Incorrect, as it squares the capacitance unnecessarily.
   • \frac{C^2 V}{2}: Incorrect, as it involves both squaring the capacitance and not squaring the voltage.
   • \frac{CV^2}{2}: Correct, as it accurately represents the potential energy formula.

Therefore, the correct formula for the energy stored in a capacitor of capacity C and potential V is \frac{CV^2}{2}.