Problema 51-5    Source:  Example 13.3 - page 282 - HUGHES, Austin -    Book: Electrical and Electronic Technology - 10ª Edição - Ed. Pearson - 2008.

Express in rectangular notation the admittance of circuits having the following impedances:

a) (4 + j 6)   Ω

b) 20 ∠ -30°   Ω

Solution of the Problem 51-5   

Item a   

Let's determine the admittance for the impedance (4 + j 6)   Ω. We know that the admittance is the inverse of the impedance. So, we can write:

Based on complex number theory, to solve this equation we must multiply and divide it by the complex conjugate of the denominator. In this way, we get:

Separating the real part from the imaginary and performing the calculation, we obtain:

Item b   

In this case, we have the impedance expressed in phasor form. Then, applying the concepts learned in the theoretical part, we can write:

However, we know that cos (-x) = cos (x) and that sin (-x) = - sin (x). Then, using these properties trigonometric we can write:

Carrying out the calculation, we have:

Now, applying the inverse of the impedance, we have:

Separating the real part from the imaginary and performing the calculation, we obtain: