Answer
(a) $f = 50~Hz$
(b) $C = 4.77~\mu F$
Work Step by Step
(a) We can find the emf frequency $f$:
$f = \frac{1}{period}$
$f = \frac{1}{0.02~s}$
$f = 50~Hz$
(b) We can write an expression for the capacitance:
$I_0 = \omega ~C~\epsilon_0$
$I_0 = 2\pi~f ~C~\epsilon_0$
$C = \frac{I_0}{2\pi~f ~\epsilon_0}$
We can find the capacitance:
$C = \frac{I_0}{2\pi~f ~\epsilon_0}$
$C = \frac{15\times 10^{-3}~A}{(2\pi)~(50~Hz) ~(10~V)}$
$C = 4.77\times 10^{-6}~F$
$C = 4.77~\mu F$
