What is the formula for calculating impedance in a series circuit?

The formula for calculating impedance in a series circuit involves both resistance (R) and reactance (X). When you have a circuit that contains resistance and capacitive reactance, the total impedance (Z) can be found using the Pythagorean theorem, which is represented mathematically as the square root of the sum of the squares of the resistance and the reactance.

In this scenario, the reactance is represented by Xc (capacitive reactance). The impedance formula thus becomes:

Z = √(R² + (Xc)²)

This formula allows you to understand how both the resistance and the reactance contribute to the overall impedance in the circuit. The reason this method works is that in an AC circuit, resistance does not vary with frequency, while reactance does, and the two components behave quite differently when current flows.

Other methods, including the addition or multiplication of R and Xc, don't provide the correct total impedance because they don't account for the angular relationship between resistance and reactance in an AC circuit. Therefore, combining R and Xc linearly or performing a multiplication does not yield a meaningful representation of how these components interact in terms of impedance.