Impedance Triangles

Resistance and Reactance Form Impedance

The magnitude model uses an exact right triangle. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Resistance and reactance are triangle legs

Resistance is 3 ohms and reactance magnitude is 4 ohms.

R=3 Ω,X=4 ΩR=3\ \Omega,\quad X=4\ \Omega
Impedance triangleThe triangle legs are checked.RXZ

The impedance magnitude closes the triangle

The checked magnitude is 5 ohms because 3 squared plus 4 squared equals 5 squared.

32+42=523^2 + 4^2 = 5^2
Magnitude checkThe impedance vector is the checked resultant.RXZ