Question

A \(12\,pF\) capacitor is connected to a \(50\,V\) battery. The electrostatic energy stored in the capacitor is:

• A. \(2.5\times10^{-6}\,J\)
• B. \(3.5\times10^{-8}\,J\)
• C. \(2.5\times10^{-8}\,J\)
• D. \(1.5\times10^{-8}\,J\)

Hint:

Energy stored in a capacitor can be written as: \[ U=\frac{1}{2}CV^2 \] \[ U=\frac{Q^2}{2C} \] \[ U=\frac{1}{2}QV \] Use whichever form matches the given data.

Answer 1

The Correct Option is D

Step 1: Recall the energy stored in a capacitor. \[ U=\frac{1}{2}CV^2 \] where \[ C=12\,pF=12\times10^{-12}F \] and \[ V=50V \]

Step 2: Substitute the values. \[ U = \frac{1}{2} \left(12\times10^{-12}\right) (50)^2 \] \[ = \frac{1}{2} \left(12\times10^{-12}\right) (2500) \] \[ = 6\times10^{-12}\times2500 \] \[ = 15000\times10^{-12} \] \[ = 1.5\times10^{-8}\,J \]

Step 3: Identify the correct option. \[ \boxed{U=1.5\times10^{-8}\,J} \]