Question

When an air capacitor with a capacitance of 300 nF (1 {\rm nF} = 10^{-9}\;{\rm F}) is connected to a power supply, the energy stored in the capacitor is 1.95×10−5 J. While the capacitor is kept connected to the power supply, a slab of dielectric is inserted that completely fills the space between the plates. This increases the stored energy by 2.74×10−5 J.

What is the potential difference between the capacitor plates?

What is the dielectric constant of the slab?

Answer 1

With the power always connected to the same supply voltage V, that remains the potential difference between the plates. The energy stored is (1/2) C V^2. C must increase by a ratio 2.74/1.95 = 1.405

That equals the diectric constant of the gap material.