Chapter A.7, Problem 86AYU

To determine

To find: The total impedance.

Answer to Problem 86AYU

The total impedance is $\frac{7}{4}+\frac{1}{4}i$ .

Explanation of Solution

Given information:

The impedance is $Z_1=2+i,Z_2=4-3i$ .

Calculation:

The total impedance is,

  $\begin{array}{c}\frac{1}{Z}=\frac{1}{Z_1}+\frac{1}{Z_2}\\ =\frac{1}{\left(2+i\right)}\frac{\left(4-3i\right)}{\left(4-3i\right)}+\frac{1}{\left(4-3i\right)}\frac{\left(2+i\right)}{\left(2+i\right)}\\ =\frac{6-2i}{8-6i+4i-3i^2}\\ =\frac{6-2i}{11-2i}\\ Z=\frac{11-2i}{6-2i}\frac{\left(6+2i\right)}{\left(6+2i\right)}\\ =\frac{70+10i}{40}\\ =\frac{7}{4}+\frac{1}{4}i\end{array}$