Which expression correctly describes impedance magnitude?

Which expression correctly describes impedance magnitude?

• A. Z = R + X
• B. Z = R × X
• C. Z = √(R^2 + X^2)
• D. Z = V × I

Answer: (C)

In AC circuits, impedance is a complex quantity with a real part (resistance) and an imaginary part (reactance), written as Z = R + jX. To get its magnitude, imagine R and X as perpendicular components forming a right triangle; the impedance magnitude is the hypotenuse: |Z| = sqrt(R^2 + X^2). This is why the expression with the square root of the sum of squares is correct. The other forms don’t fit because adding R and X ignores the vector nature of impedance, and multiplying them has no direct meaning for impedance. Impedance relates voltage and current by Z = V/I, so its magnitude is |Z| = |V|/|I|, not V × I. Remember that X can be positive or negative depending on inductive or capacitive reactance, but in the magnitude formula it’s squared, so the sign doesn’t matter.

In AC circuits, impedance is a complex quantity with a real part (resistance) and an imaginary part (reactance), written as Z = R + jX. To get its magnitude, imagine R and X as perpendicular components forming a right triangle; the impedance magnitude is the hypotenuse: |Z| = sqrt(R^2 + X^2). This is why the expression with the square root of the sum of squares is correct. The other forms don’t fit because adding R and X ignores the vector nature of impedance, and multiplying them has no direct meaning for impedance. Impedance relates voltage and current by Z = V/I, so its magnitude is |Z| = |V|/|I|, not V × I. Remember that X can be positive or negative depending on inductive or capacitive reactance, but in the magnitude formula it’s squared, so the sign doesn’t matter.