What is the magnitude of the impedance in a series AC circuit with a resistance of 6 ohms and an inductive reactance of 17 ohms?

In a series AC circuit, the magnitude of the impedance can be determined by combining the resistance and the inductive reactance using the Pythagorean theorem. The impedance (Z) in a series circuit is calculated using the formula:

Z = √(R² + XL²)

where R is the resistance and XL is the inductive reactance.

In this scenario, the resistance (R) is 6 ohms and the inductive reactance (XL) is 17 ohms. Plugging these values into the formula gives:

Z = √(6² + 17²)

Z = √(36 + 289)

Z = √325

Z = 18.03 ohms

Rounding this value to two decimal places gives us approximately 18 ohms, making it the correct magnitude of the impedance in this AC circuit. This calculation shows how both resistance and reactance interact to form the total impedance, which is essential for understanding AC circuit behavior.