SOLUTION: Three impedances are connected in parallel. 𝑍1=2𝑗+3, 𝑍2=5−6𝑗, 𝑍3=3𝑗. Find the equivalent admittance 𝑌 where 𝑌=1/𝑍1+1/𝑍2+1/𝑍3 Express the admitt

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Three impedances are connected in parallel. 𝑍1=2𝑗+3, 𝑍2=5−6𝑗, 𝑍3=3𝑗. Find the equivalent admittance 𝑌 where 𝑌=1/𝑍1+1/𝑍2+1/𝑍3 Express the admitt      Log On


   



Question 1151107: Three impedances are connected in parallel. 𝑍1=2𝑗+3, 𝑍2=5−6𝑗, 𝑍3=3𝑗. Find the equivalent admittance 𝑌 where
𝑌=1/𝑍1+1/𝑍2+1/𝑍3
Express the admittance in both rectangular and polar forms.

Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
You need to practice this. Looks like you are studying electrical circuits. If you have tried this, please post where you are stuck or what you came up with for an answer.

For reference, one over the total (equivalent) impedance is the admittance:




Example with different impedances:
Given Z1 = 3+j and Z2 = 5+6j in parallel:
+Y+=+1%2FZ1+%2B+1%2FZ2+=+1%2F%283%2Bj%29+%2B+1%2F%285%2B6j%29+
+Y+=+%283-j%29%2F%28%283%2Bj%29%283-j%29%29+%2B+%285-6j%29%2F%28%285%2B6j%29%285-6j%29%29+
+Y+=+%283-j%29%2F10+%2B+%285-6j%29%2F61+
+Y+=+%28183-61j+%2B+50-60j%29%2F610+
+Y+=+%28223+-+121j%29+%2F+610++ mhos
or
+Y+=+0.382+-+0.198j+ mhos (to 3 decimal places)

Your problem is solved in a similar manner.


Polar form is left as an exercise:
I will give you this: Z1 = 3+2j =
= +3.6055%2Ae%5E%280.588j%29+ (angle in radians)