A 2.0 F capacitor is charged to a potential difference of 12 V and is subsequently connected to an uncharged 4.0 F capacitor. Determine the heat produced during the charge transfer from one capacitor to the other.

Step-by-step solution

Given: C₁ = 2.0 F V₁ = 12 V C₂ = 4.0 F V₂ = 0 V The heat produced during the charge transfer is equal to the loss in electrostatic potential energy of the system: H = 1 2 C₁ C₂ C₁ + C₂ (V₁ - V₂)^2 Substituting the given values: H = 1 2 2.0 4.0 2.0 + 4.0 (12 - 0)^2 J H = 1 2 8.0 6.0 144 J H = 4 6 144 J = 96 J