The complex impedance cartesian form approximately

Solved Step by Step With Explanation-Complex Impedance Calculations

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Solved Step by Step with Explanation-Complex Impedance Calculations

• Z is the complex impedance.

• R is the resistance (50Ω in this case).

ω=2π×frequency=2π×50Hz=100πrad/s

Now, substitute the values into the formula:

θ=arctan(RωL​)

Substitute the values and calculate:

Z2​=1+3j

In a parallel combination, the formula for the total impedance

Z=1/1/5−6j​+1/1+3j​

Simplify the expression in the denominator by finding a common denominator and adding the fractions. Then, take the reciprocal to find Z in Cartesian form (real + imaginary):

Z=112−(3j)2−77+21j​=121+9−77+21j​=2.46+2.73j

So, the complex impedance Z in Cartesian form is approximately 2.46+2.73j.