Question

You insert a dielectric into an air-filled capacitor. How does this affect the energy stored in the capacitor?

a) Increases.

b) Decreases.

c) Remains unchanged.

d) Depends on the dielectric constant.

Answer 1

Inserting a dielectric into an air-filled capacitor decreases the energy stored in the capacitor due to the dielectric reducing the internal electric field strength and therefore the voltage across the plates for the same charge.

Step-by-step explanation:

When you insert a dielectric into an air-filled capacitor, the energy stored in the capacitor decreases. This occurs because the dielectric reduces the electric field strength inside the capacitor, resulting in a lower voltage across the plates for the same amount of charge. Since the energy (U) stored in a capacitor is given by U = 1/2 CV^2, where C is the capacitance and V is the voltage, reducing the voltage while capacitance increases (as C = Q/V, with Q being the charge and a larger C resulting from the lower V for the same charge) leads to a decrease in energy stored.

The energy is used to polarize the dielectric, which aligns the molecules inside the dielectric material, and this polarization effectively reduces the electric field within the capacitor. If the dielectric is removed, the stored energy increases again because the electric field strength is restored to its original value, and the voltage across the capacitor plates increases for a given charge.