Question

Two batteries of emf ξ₁ and ξ₂ a capacitor of capacitance C, and a resistor

of resistance R are connected in a circuit as shown in Fig. 101.

Determine the amount of heat Q liberated in the resistor after switching the key K.

Answer 1

Before switching the key K, the charge on the capacitor is q₁ = ξ₁C, the positive charge being on the lower plate, and the negative charge, on the upper plate.

After switching the key K, as a result of recharging, the upper plate will acquire a positive charge, and the lower plate a negative charge equal to q₂ = ξ₂C.

Thus, the current source of emf ξ₂ will do the work ξ₂(q₁ + q₂). The required amount of heat liberated thereby in the resistor is