Consider the circuit shown in the figure, where the ac source voltage is given by $v(t)=V_{n}sin(t).$

$($a$)(8$ Pts$.)$ What is the total impedance?

$($b$)(10$ Pts$.)$ Find the current $i_R(t)$ through the resistor.

$($c$)(7$ Pts$.)$ What is the average power dissipated in the circuit?

Solution:

Voltage across the capacitor is equal to the voltage across the inductor, because they are

connected in parallel. Denoting by $V_1$ the amplitude of this voltage, let us draw the phasor

diagram assuming $x_C>x_L{x}_C.$ The formulas will $be$ valid for $x_C>x_{L}as$ well. $We$ have the

following relations: