Parallel circuits. If the two resistors in Exercise 1 are connected in parallel, the total...

Parallel circuits. If the two resistors in Exercise 1 are connected in parallel, the total impedance is given by

Find the total impedance assuming that the resistors in Exercise 1 are connected in parallel.

As with impedance, the current I and voltage V in a circuit can be represented by complex numbers. The three quantities (voltage, V; impedance, Z; and current, I) are related by the equation . Thus, if two of these values are given, the value of the third can be found from the equation.

Exercise 1

Series circuits. Assuming that the impedance of a resistor in a circuit is Z1 = 4 + 3i ohms and the impedance of a second resistor is Z2 = 5 – 2i ohms, find the total impedance of the two resistors when placed in series (sum of the two impedances).