Which of the following expressions represents the inductive reactance in polar coordinates?

• A. $X=R\angle 0°$
• B. $X=\omega L\angle 0°$
• C. $X=\frac{1}{\omega C}\angle -90°$
• D. $X=\omega L\angle 90°$

Answer: (D)

Verified step by step guidance

1. Recall that inductive reactance \(X_L\) is the opposition to the change of current by an inductor in an AC circuit, and it is given by the formula \(X_L = \omega L\), where \(\omega\) is the angular frequency and \(L\) is the inductance.
2. Understand that in polar form, a purely inductive reactance has a magnitude equal to \(\omega L\) and a phase angle of \(+90^\circ\) because the voltage across an inductor leads the current by 90 degrees.
3. Express the inductive reactance in polar coordinates as \(X = \omega L \angle 90^\circ\), where \(\angle\) denotes the phase angle.
4. Compare this with the given options: the expression with \(X = \omega L \angle 0^\circ\) represents a purely resistive element, and \(X = \frac{1}{\omega C} \angle -90^\circ\) represents capacitive reactance.
5. Conclude that the correct polar form for inductive reactance is the one with magnitude \(\omega L\) and phase angle \$90^\circ\(, i.e., \)X = \omega L \angle 90^\circ$.