For the Circuit Shown Below, Let (A) Find Impedances $Z _ { \mathrm { R } 1 } , Z _ { L 1 } , Z _ { R 2 }$

Essay

for the circuit shown below, let $\mathrm { vs } ( \mathrm { t } ) = 457 \cos \left( 2 \pi 60 \mathrm { t } - 110 ^ { \circ } \right) \mathrm { V } , \mathrm { R } _ { 1 } = 20 \Omega , \mathrm { R } _ { 2 } = 65 \Omega , \mathrm { L } _ { 1 } = 35 \mathrm { mH } , \mathrm { L } _ { 2 } = 85 \mathrm { mH } , \mathrm { C } = 95 \mu \mathrm { F }$
(a) Find impedances $Z _ { \mathrm { R } 1 } , Z _ { L 1 } , Z _ { R 2 }$ , ZL2, Z $Z _ { C }$ and phasor $V _ { S }$ for vs(t).
(b) Find the equivalent impedance $Z _ { a }$ of parallel combination of $Z _ { R 2 } + Z _ { L 2 }$ and $Z _ { C }$ .
(c) Find the total impedance $Z _ { t }$ seen from the voltage source.
(d) Find the phasor for the current I.
(e) Find the phasor for $V _ { C }$ across the capacitor.
(f) Find $v _ { C } ( t )$ .