A parallel$-$plate capacitor with vacuum between its horizontal plates has a capacitance of $22\mathrm{.}0$F$.$ A nonconducting liquid with dielectric constant $4\mathrm{.}90$ is poured into the space between the plates, filling up a fraction f of its volume.

$($a$)$ Find the new capacitance as a function of f$.($Cf is in $$F$.$ Use any variable or symbol stated above as necessary.$)$

Cf $=$

$$$2210\mathrm{.}80$

$($b$)$ What should you expect the capacitance to be when f $=0?$

$22$

$22$

$$F

Does your expression from part $($a$)$ agree with your answer?

YesNo$$

$($c$)$ What capacitance should you expect when f $=1?$

$107\mathrm{.}8$

$108$

$$F

Does the expression from part $($a$)$ agree with your answer?

YesNo$$