Question

What is the total impedance of two resistors connected in parallel, given that the resistors have impedances of Z1​=6+5i ohms anZ2=7−2i ohms?

Answer 1

The total impedance of two resistors connected in parallel, with impedances of Z1​=6+5i ohms and Z2=7−2i ohms, can be found using the formula Ztotal = 1/((1/Z1) + (1/Z2)). By substituting the given values, simplifying, and expanding, we find that the total impedance is (47 + 28i)/(13 + 3i) ohms.

Step-by-step explanation:

The total impedance of two resistors connected in parallel is given by the formula:

Ztotal = 1/((1/Z1) + (1/Z2))

Using the given values:

Z1 = 6 + 5i ohms
Z2 = 7 - 2i ohms

we can substitute the values into the formula to get:
Ztotal = 1/((1/(6 + 5i)) + (1/(7 - 2i)))

Simplifying the expression, we multiply the numerator and denominator by the conjugate of the denominator to eliminate the complex numbers:

Ztotal = (6 + 5i)(7 - 2i) / ((6 + 5i) + (7 - 2i))

Expanding and combining like terms, we get:

Ztotal = (47 + 28i)/(13 + 3i)

Therefore, the total impedance of the two resistors connected in parallel is (47 + 28i)/(13 + 3i) ohms.