Question

a parallel-plate has a capacitance of 25.0 uF. a nonconducting liquid with dielectric constant 6.50 is poured into the space between the plates, filling up a afractiom f of its volume a) Find the new capacitance as a function of f. b) when should you expect the capacitance to be when f=0? does your expression from part? a) agree with your answer? c) what capacitance should you expect when f=1? does the expression from part a) agree with your answer?

Answer 1

(a)

$С=С_1+С_2$

$С_1=\frac{\epsilon \epsilon_0Sf}{d}$

$С_2=\frac{\epsilon_0S(1-f)}{d}$

$C=\frac{\epsilon\epsilon_0Sf}{d}+\frac{\epsilon_0S(1-f)}{d}=\frac{\epsilon_0S}{d}(1+f(\epsilon-1))$

(b)

if $f=0$

$C=\frac{\epsilon_0S}{d}(1+f(\epsilon-1))=\frac{\epsilon_0S}{d}$

(c)

if $f=1$

$C=\frac{\epsilon_0S}{d}(1+f(\epsilon-1))=\frac{\epsilon\epsilon_0S}{d}$