What is the impedance in a circuit with a resistance of 10 ohms and an inductive reactance of 15 ohms?

To find the impedance in a circuit that includes resistance and inductive reactance, you can use the formula for impedance in an AC circuit, which is given by:

Z = √(R² + X_L²)

Where Z is the impedance, R is the resistance, and X_L is the inductive reactance.

In this scenario, the resistance (R) is 10 ohms, and the inductive reactance (X_L) is 15 ohms. Plugging these values into the formula gives us:

Z = √(10² + 15²)

Z = √(100 + 225)

Z = √325

Z ≈ 18.0277 ohms

This result represents the total opposition that the circuit presents to the current, which consists of both the resistance and the inductive reactance. This is why the answer, approximately 18.0277 ohms, is correct; it accurately reflects the combined effect of both components in the circuit.