Question

A dielectric of dielectric constant 5.0 is filled in the gap between the plates of a capacitor.calculate the factor by which the capacitance is increased,if the dielectric is only sufficient to fill up 1/5 of the gap.

Answer 1

$C_0=\frac{\epsilon_0S}{d}$

$C=C_1+C_2=\frac{\epsilon\epsilon_0(1/5)S}{d}+\frac{\epsilon_0(4/5)S}{d}=$

$=\frac{\epsilon_0S}{d}(\epsilon/5+4/5)$ .

$k=\frac{C}{C_0}=\epsilon/5+4/5=5/5+4/5=1.8$ .Answer