A variable capacitor with a range from $10$ pF $($C$10)$ to $365$ pF $($C$365)$ is used with a coil to tune the input to an AM radio. $($a$)$ What ratio of maximum to minimum frequencies may be tuned with such a capacitor? $($b$)$ If this capacitor is to tune from $0\mathrm{.}54$ MHz to $1\mathrm{.}6$ MHz$,$ the ratio computed in $($a$)$ is too large. By adding a $($padding$)$ a capacitor $($C$)$ in parallel to the variable capacitor this range may be adjusted. How large should this capacitor be and $($c$)$ what inductance L should be chosen in order to tune the desired range of frequencies?