Problem $1.(15)$

For the circuit shown, LI is absorbing $20$ kVA at power factor $0\mathrm{.}8($lagging$)$ and L$2$ absorbs $9$ KW of power at $0\mathrm{.}6($leading$).$

Find: $($a$)P_1,Q_1$ and $S_1$

$($b$)P_2,Q_2,S_2$

$($c$)$ Effective Power factors of the two loads in parallel

$($d$)$ Currents $I_1$ and $I_2$

Problem $2.(10)$

a$)$ For the circuit shown, determine the impedance $($ ZL $)$ that results in maximum average power transfer b$)$ What is the maximum average power transferred to the load impedance determined in part $($a$)$

Problem $3(10)$

For the circuit shown, determine the values of following :

a$)H(s)$

b$)$ Center frequency $(f_0)$

c$)$ Cut off frequencies $(f{c}_1$ and $f{c}_2)$

d$)$ Bandwidth $($b$)$

e$)$ Quality factor $($Q$)$

From $($b$-$e$,$ use the formula sheet$)$

Problem $4(15)$

For the circuit shown, determine

$($a$)$ the $I_1($s$)$ and $I_2($s$)$ using Cramer's Rule

$($b$)$ Find $i_1(t)$ and $i_2(t)$ using Laplace Inverse transformation