What method is used to calculate total impedance in an alternating current circuit?

The correct method to calculate total impedance in an alternating current circuit is based on the right triangle method. This method utilizes the relationship between resistance (R), inductive reactance (X_L), and capacitive reactance (X_C) by representing these components as the sides of a right triangle.

In a right triangle, the total impedance (Z) serves as the hypotenuse, whereas the resistance and the net reactance (which is the difference between inductive and capacitive reactance) form the other two sides. The total impedance is then calculated using the Pythagorean theorem:

[ Z = \sqrt{R^2 + (X_L - X_C)^2} ]

This approach provides a clear visual representation of how resistance and reactance interact in AC circuits, making it easier to comprehend the concept of impedance as a vector quantity. By breaking down the circuit elements into their respective components, one can accurately determine the overall impedance, which is crucial for understanding circuit behavior and for effective troubleshooting.

In contrast, other methods like the quadratic, sine wave, and graphical methods may not provide the clarity and direct relationship between the components when calculating impedance. They may serve well in other contexts but are not typically employed for this specific purpose