If the frequency of an AC source is doubled, what happens to the inductive react
Practice Questions
Q1
If the frequency of an AC source is doubled, what happens to the inductive reactance of an inductor? (2021)
It doubles
It halves
It remains the same
It quadruples
Questions & Step-by-Step Solutions
If the frequency of an AC source is doubled, what happens to the inductive reactance of an inductor? (2021)
Step 1: Understand that inductive reactance (Xl) is calculated using the formula Xl = ωL, where ω (omega) is the angular frequency and L is the inductance.
Step 2: Recognize that angular frequency (ω) is related to the frequency (f) of the AC source by the formula ω = 2πf.
Step 3: If the frequency (f) is doubled, then the new frequency is 2f.
Step 4: Calculate the new angular frequency: ω' = 2π(2f) = 4πf, which means the angular frequency has also doubled.
Step 5: Substitute the new angular frequency into the inductive reactance formula: Xl' = ω'L = 4πfL.
Step 6: Compare the new inductive reactance (Xl') with the original inductive reactance (Xl = 2πfL). You will see that Xl' = 2 * Xl.
Step 7: Since Xl' is double the original Xl, we can conclude that if the frequency is doubled, the inductive reactance halves.
