Concepts Of Physics MCQ Edition [Volume 2]PhysicsCapacitors
A parallel-plate capacitor with a plate area of 20 cm ^2 and a separation of 1.00 mm between the plates is connected to a 12.0 V battery. The plates are subsequently pulled apart to increase the separation to 2.0 mm . Which of the following statements correctly describes the heat produced during this transfer of charge as the separation is increased?
Options
- AHeat is produced because the work done by the person is entirely dissipated as thermal energy.
- BHeat is produced because the energy absorbed by the battery is less than the decrease in the stored energy of
- CNo heat is produced because the process occurs isothermally and the battery does zero work.
- DNo heat is produced because the work done by the person plus the initial stored energy equals the final stored
Correct answer
D. No heat is produced because the work done by the person plus the initial stored energy equals the final stored
Step-by-step solution
Let the initial capacitance be C_i = ₀ A d . When the separation is increased to 2d , the final capacitance becomes C_f = ₀ A 2d = C_i 2 . The initial stored energy in the capacitor is U_i = 1 2 C_i V^2 . The final stored energy is U_f = 1 2 C_f V^2 = 1 4 C_i V^2 . The initial charge on the capacitor is Q_i = C_i V and the final charge is Q_f = C_f V = C_i V 2 . Since the charge decreases, charge flows back to the battery. The energy absorbed by the battery is Q V = (C_i V - C_i V 2 ) V = 1 2 C_i V^2 . The attracti