Question

an inductor with inductance l is connected in series with an ac source that provides a sinusoidal voltage of v of t is equal to v times cosine of begin quantity omega times t end quantity, where v is the maximum voltage, omega is the angular frequency, and t is the time. if the angular frequency of the ac source is increased from omega to 3 times omega, what happens to the inductive reactance, xl?

Answer 1

Increasing the angular frequency of an AC source by a factor of three causes the inductive reactance (XL) of an inductor to triple because XL is directly proportional to frequency.

Step-by-step explanation:

Inductive reactance is the name given to the opposition to a changing current flow. This impedance is measured in ohms, just like resistance. In inductors, voltage leads current by 90 degrees.

When an inductor with inductance L is connected to an AC source, and the frequency of the AC source is increased, the inductive reactance, XL, increases proportionally.

The formula for inductive reactance is given as XL = 2πfL, where f is the frequency in hertz, L is the inductance, and 2π represents the full cycle of the sinusoidal wave in radians.

Since the inductive reactance is directly proportional to the frequency, if the angular frequency ω is increased from ω to 3ω, the inductive reactance XL will triple.