Impedance triangle for series RC circuits In the right-triangle (phasor) representation of a series RC circuit with sides R and |XC|, what does the hypotenuse represent?

Introduction / Context:
Engineers often visualize the relationship between resistance and reactance using a right triangle known as the impedance triangle. This geometric view clarifies how magnitudes combine and how phase angle arises in AC circuits.

Given Data / Assumptions:

• Series RC circuit with resistance R and capacitive reactance magnitude |XC|.
• Right triangle drawn with adjacent side R and opposite side |XC|.
• Phasor convention: current is the reference axis for series analysis.

Concept / Approach:
For series RC, the complex impedance is Z = R − j|XC|. The magnitude is |Z| = sqrt(R^2 + |XC|^2). When represented as a right triangle, the legs are R and |XC|, and the hypotenuse is |Z|, the magnitude of the impedance. The angle between the hypotenuse and the R-axis equals the phase angle.

Step-by-Step Solution:

Verification / Alternative check:
Ohm’s law for phasors states V = I * Z. If the current magnitude is 1 A, the voltage magnitude equals |Z| volts. That ties the hypotenuse length directly to the observed voltage magnitude for unit current, reinforcing that it represents |Z|.

Why Other Options Are Wrong:

Common Pitfalls:
Swapping series and parallel triangles; forgetting that capacitive reactance is plotted on the negative imaginary axis, though magnitude is used for the triangle.

Final Answer:
impedance