Find the admittance Yab in the circuit seen in the figure Ta

Find the admittance Yab in the circuit seen in the figure. Take that R1 = 6 , R2 = 6 , R3 = 4 and R4 = 12.8

Part A

Express Yab in rectangular form.

Express your answer in complex form.

The answer is NOT

Yab = (4+j3)10^(5) mS

Yab = 40+j30 mS

510^(5) e^(j36.86)

Solution

Z3=R3||j10=4*j10/(4+j10)

Z2=R2+j12=6+j12

Z1=R1-j2=6-j2

Zequ1=Z1||Z2||Z3=2.1517 +j 0.5793

Z=R4+Zequ1-j12.8=12.8-j12.8+2.1517 + j0.5793=14.9517 -j12.2207

Y=1/Z=1/14.9517 -j12.2207

Y=0.0401 + j0.0328

convert rect to polar

a=sqrt((0.0401^2)+(0.0328^2))=0.0518

b=tan^-1(-0.0328/0.0401)=- 0.6856 in radins, if conver to degree=-39.2

ans:

0.051806*exp^j-39.2