Question

The energy stored in a capacitor has a value U when connected to a battery with a voltage V. When the voltage is increased to 2V, the energy stored in the capacitor is:

Answer 1

The energy stored in the capacitor when the voltage is increased to 2V is 4U

Data obtained from the question

• Initial voltage (V₁) = V

• Initial energy (E₁) = U

• Final voltage (V₂) = 2V

• Final energy (E₂) =?

Determination of the energy

Energy stored in a capacitor is given by

E = ½CV²

If the capacitor, C is constant, then

E₁ / V₁² = E₂ / V₂²

U / V² = E₂ / (2V)²

U / V² = E₂ / 4V²

Cross multiply

V² × E₂ = U × 4V²

Divide both side by V²

E₂ = (U × 4V²) / V²

E₂ = 4U

Therefore, the final energy in the capacitor will be 4U

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