Question

The work done in placing a charge of \( 8 \times 10^{-18} \) coulomb on a capacitor of capacitance 100 microfarad is:

• A. \( 3.1 \times 10^{-26} \) joule
• B. \( 4 \times 10^{-10} \) joule
• C. \( 32 \times 10^{-32} \) joule
• D. \( 16 \times 10^{-32} \) joule

Hint:

The formula \( W = \frac{Q^2}{2C} \) is useful for calculating the energy stored in a capacitor when charge and capacitance are known.

Answer 1

The Correct Option is C

Step 1: Formula for work done in charging a capacitor 
The work done \( W \) in charging a capacitor is given by: \[ W = \frac{Q^2}{2C} \] where: \( Q = 8 \times 10^{-18} \) C (charge), \( C = 100 \times 10^{-6} \) F (capacitance). 
Step 2: Substituting values 
\[ W = \frac{(8 \times 10^{-18})^2}{2 \times (100 \times 10^{-6})} \] \[ = \frac{64 \times 10^{-36}}{2 \times 100 \times 10^{-6}} \] \[ = \frac{64 \times 10^{-36}}{200 \times 10^{-6}} \] \[ = 32 \times 10^{-32} { joule} \]