Question

The textbook is Physics for science and engineers by Knight 3rd edition.

Section 29.7 of the text derives/explains what happens to the capacitance C_0 of an air-gap parallel plate capacitor if a dielectric fills the gap (distance = d) between the plates. What is the new capacitance if a dielectric of constant k only half-fills the space? Derive C in terms C_0, k.

Answer 1

If half of the space fills with another dielectric then its capacitance would be
= kC_o / 2
and remaining capacitance would be C_o/2
Now both of these capacitance would be in Parallel therefore
Net capacitance
= C_o/2 + kC_o /2 = (C_o /2 )(1+k)