$($b$)$ A $33$ mF capacitor is charged by a $24$ V battery. i$)$ How much charge is build up across its plates?

ii$)$ If the capacitor has a temperature coefficient or $ppm$ of $-180pp\frac{m}{}C,$ what is the capacitance of the capacitor if the temperature increases by $40C.$

$(10$ marks$)$

$($c$)$ 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 $x_C.$ Round values to $3$ decimal place.

iii. Evaluate the total impedance $(Z_T)$ of the circuit, and the phase angle $({}_T)$ for the circuit. Does the source voltage lead the source current?

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.