Question

The INCORRECT formula representing the energy stored in a parallel plate capacitor in usual notation is

• A. $\dfrac{1}{2}CV^2$
• B. $\dfrac{Q^2}{2C}$
• C. $\dfrac{1}{2}QV$
• D. $\dfrac{1}{2}\dfrac{Q}{V}$
• E. $\dfrac{1}{2}\varepsilon_0E^2 \times \text{Volume}$

Hint:

Physics Tip: Always check units. Energy must have unit Joule. If an expression gives Farad, Volt, or Coulomb only, it cannot represent stored energy.

Answer 1

The Correct Option is D

Concept:
The electrostatic energy stored in a capacitor can be written in several equivalent forms using the relations: $$Q = CV,\qquad V = \frac{Q}{C}$$
Step 1: Write the standard energy formulas.
For any capacitor: $$U=\frac{1}{2}CV^2=\frac{Q^2}{2C}=\frac{1}{2}QV$$ These are the valid expressions for stored energy. :contentReference[oaicite:0]{index=0}
Step 2: Check option (D).
Given: $$\frac{1}{2}\frac{Q}{V}$$ But since: $$\frac{Q}{V}=C$$ So option (D) becomes: $$\frac{1}{2}C$$ This has unit of capacitance, not energy. Hence it is incorrect.
Step 3: Check option (E).
Energy density in electric field: $$u=\frac{1}{2}\varepsilon_0E^2$$ Total energy: $$U=u \times \text{Volume}$$ So option (E) is correct for a parallel plate capacitor.
Therefore, the incorrect formula is Option (D). :contentReference[oaicite:1]{index=1}