Reactance and Inductance of an inductor

[Kathi201]

a. The reactance of an inductor is 100 ohms at 2kHz. What is the inductance of this inductor??

b. At what frequency is the reactance of a 3.5-mH inductor equal to 10 ohm?


I am not even sure what equations to use for these two questions. I know that for a the inductive reactance equation is XL = wL, but here I have two unknowns, XL and w so I am not sure what equation to use. For b the frequency equation I have is w = 1/LC but I do not know the capacitance.

If anyone knows the equations that I would use for these two I would appreciate the help ASAP! :)

 

[marcusl]

a) you have only one unknown because the angular frequency [tex] \omega[/tex] is simply related to frequency by [tex]\omega=2\pi f[/tex] .

b) Use the same inductance equation--not the capacitance equation you wrote down for b)!--solving this time for frequency.

 

[thomate1]

I can provide some insights on these questions.

a. The reactance of an inductor is given by the equation XL = 2πfL, where XL is the inductive reactance in ohms, f is the frequency in Hertz, and L is the inductance in Henrys. So, for the given reactance of 100 ohms and frequency of 2kHz, we can rearrange the equation to solve for L: L = XL/(2πf) = 100/(2π*2000) = 0.0159 Henrys.

b. To find the frequency at which the reactance of a 3.5-mH inductor is equal to 10 ohms, we can use the same equation XL = 2πfL and plug in the values: 10 = 2πf*3.5*10^-3. Solving for f, we get f = 10/(2π*3.5*10^-3) = 4.53kHz.

I hope this helps! It's important to note that these equations are based on ideal conditions and may vary in real-world scenarios. Factors such as resistance and capacitance can affect the reactance and inductance of an inductor.