Question

The energy stored in a capacitor of capacitance \( 10 \, \mu\text{F} \) when charged to a potential of 6 kV is

• A. 100 J
• B. 200 J
• C. 180 J
• D. 160 J
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Hint:

Calculate capacitor energy with \( U = \frac{1}{2} C V^2 \); ensure consistent SI units.

Answer 1

The Correct Option is C

The energy stored in a capacitor is: \[ U = \frac{1}{2} C V^2 \] Given \( C = 10 \, \mu\text{F} = 10 \times 10^{-6} \, \text{F} \), \( V = 6 \, \text{kV} = 6 \times 10^3 \, \text{V} \): \[ V^2 = (6 \times 10^3)^2 = 36 \times 10^6 \, \text{V}^2 \] \[ U = \frac{1}{2} \cdot (10 \times 10^{-6}) \cdot (36 \times 10^6) = \frac{1}{2} \cdot 10 \cdot 36 = 180 \, \text{J} \] Alternative formula: \( U = \frac{1}{2} Q V \), where \( Q = C V \): \[ Q = (10 \times 10^{-6}) \cdot (6 \times 10^3) = 60 \times 10^{-3} \, \text{C} \] \[ U = \frac{1}{2} \cdot (60 \times 10^{-3}) \cdot (6 \times 10^3) = \frac{360}{2} = 180 \, \text{J} \] Check options: - (1) 100 J: Incorrect.
- (2) 200 J: Incorrect.
- (3) 180 J: Correct.
- (4) 160 J: Incorrect.
Option (3) is correct.