Question $(1)4$ Marks

For the sinusoidal $v$ and $i,$ it is required to find out:

a$)$ the sinusoidal expression for the voltage $v(t)$ and current $i(t).$

b$)$ the impedance $Z.$

c$)$ the power factor $(F_P).$

d$)$ the power $($ P $)$ in watts.

Question $(2)4$ Marks

Find the series element or elements that must be in the closed container to satisfy the following conditions.

$q,$

$V=I{R}^{(b)}$ Circuit has a lagging power factor.

$R=\frac{V}{\text{I}}$ Question $(3)4$ Marks

a$)$ Find the value of impedance $Z_{ab}$ that need to be placed

Yo beween termanal a and b for maximum power transfer to it$.$

b$)$ What is the maximum power transfer to $Z_{ab}?$

Question $(4)4$ Marks In this circuit shown in the circuit, find the following:

a$)$ total number of watts $($P$),$ voltamperes reactive $($Q$),$ volt$-$amperes $($S$),$

b$)$ power factor $(F_p).$

c$)$ source current $I_s.$

d$)$ impedance in each box.

$v=24$

Question $(5)4$ Marks Given the circuit shown,

a$)$ Find voltages Va and $V_b$

b$)$ Determine a new value for the $2$ k resistor such that $V_b$ is $12$ volts.