$($b$)$ If a $150$ mF capacitor has a temperature coefficient or ppm of $-200pp\frac{m}{}C,$ what is the capacitance it the capacitor if the temperature increases by $20C.$

$(5$ marks$)$

$($c$)$ How much energy is stored by an ideal capacitor, rated at $470F,$ if a DC voltage supply of $48$ V is placed across it$.$ How much of the energy is dissipated in the ideal capacitor?

$(5$ marks$)$

$($d$)$ The RLC circuit is supplied by an AC voltage source with a phase offset of zero.

$(15$ marks$)$

i$.$ If the peak value of the signal is $325\mathrm{.}27$ V $,$ calculate the RMS value of the source voltage.

ii$.$ Convert the inductance and capacitance values to reactance $()$ and draw the resulting impedance diagram for $R,x_L$ and $x_C.$

iii. Evaluate the total impedance $(Z_T)$ of the circuit, and the phase angle $({}_T)$ for the circuit.

iv$.$ Calculate the current in the circuit and its phase angle.

v$.$ Evaluate the voltage across the resistor, capacitor, and inductor, and draw these on a phasor diagram.