In the circuit shown below, let $E_0=11\mathrm{.}5V,R=3\mathrm{.}27,$ and $L=0\mathrm{.}565H.$ The switch is closed at time $t=0.$ During the time from $t=0$ to $t=\frac{L}{R}$ find the following. Hint: Find the energy transfer rates as functions of time and integrate.

$($a$)$ the amount of energy supplied by the battery

$$ J

$($b$)$ the amount of energy dissipated in the resistor

$$

$($c$)$ the amount of energy delivered to the inductor

$$