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Given the equivalent impendance of a circuit can be calculated…

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Given the equivalent impendance of...
Given the equivalent impendance of a circuit can be calculated by the expression
Z=Z1Z2/ Z1+Z2
If Z1= 4+j10 and Z2=12-j3, calculate the impendance Z in both rectangular and polar forms.
Submitted: 3 years ago.Category: Calculus and Above
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6/20/2015
Tutor: Sandhya_sharma, Master's Degree replied 3 years ago
Sandhya_sharma
Sandhya_sharma, Master's Degree
Category: Calculus and Above
Satisfied Customers: 3,782
Experience: I hold M.Sc and M.Phil degrees in math and have several years of teaching experience.
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Z1Z2 = (4+10j)(12-3j) = 48+120j-12j-30j^2 = 48+120j-12j+30 = 78+108j
Z1+Z2 = (4+10j)+(12-3j) = 16+7j
Z=Z1Z2/ Z1+Z2
= (78+108j)/(16+7j)
= (78+108j)(16-7j)/(16+7j)(16-7j)
= (2004+1182j)/(16^2-49j^2)
= (2004+1182j)/(256+49)
= (2004+1182j)/305
= 2004/305 + (1182/305)j
rectangular form for Z is 2004/305 + (1182/305)j
I will send rest of the solution in 10-15 minutes.
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Tutor: Sandhya_sharma, Master's Degree replied 3 years ago
Let us convert it to polar form now:
r = SQRT((2004/305)^2 + (1182/305)^2) = 7.628
Angle Thetha = arctan (1182/2004) = 30.5 degrees
polar form is (7.628, 30.5 degrees)
I hope it will help you.
Please don't forget to rate my answer!
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