Frequency where reactence is zero

In summary, the question asks at what frequency are the reactances of a 58 mH inductor and a 84 µF capacitor equal. The equations for the reactances are Xl=1/2(Pi)fL and Xc=2(Pi)fC. By setting the two equations equal to each other, we get 1/2(Pi)fL=2(Pi)fC. Solving for f, we get a frequency of 1/2(Pi)(LC)^(-1/2), where L=58mH and C=84µF.
  • #1
kdrobey
27
0

Homework Statement


At what frequency (in Hz) are the reactances of a 58 mH inductor and a 84 µF capacitor equal?


Homework Equations


Xl=1/2(Pi)fL
Xc=2(Pi)fC



3. The Attempt at a Solution [/b
F needs to be the same for both, so i got f by itself in both equations, then had them equal each other, giving me Xl2(Pi)L=1/2(Pi)XcC, but I am stuck from there
 
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  • #2
kdrobey said:

Homework Statement


At what frequency (in Hz) are the reactances of a 58 mH inductor and a 84 µF capacitor equal?

Homework Equations


Xl=1/2(Pi)fL
Xc=2(Pi)fC
3. The Attempt at a Solution [/b
F needs to be the same for both, so i got f by itself in both equations, then had them equal each other, giving me Xl2(Pi)L=1/2(Pi)XcC, but I am stuck from there

I think you have misunderstood the question. The question wants to know for what frequencies are the reactances the same. In other words, find f such that Xc = Xl.
 
  • #3
so if Xl=Xc, then 1/2(Pi)fl=2(Pi)fC? i tried that then got 1=(2pi fL)*(2pi fC). is that on the right track?
 
  • #4
Yes, now just solve for f.

On a related note, wikipedia tells me
Xc = 1 / (2pi*f*C)
Xl = 2*pi*f*L
Which seems to be the opposite of what you have written, although it should still give the same answer.
 
  • #5
kdrobey said:
so if Xl=Xc, then 1/2(Pi)fl=2(Pi)fC? i tried that then got 1=(2pi fL)*(2pi fC). is that on the right track?
Looks good thus far :approve:.
 
  • #6
got it! thanks a lot
 
  • #7
kdrobey said:
got it! thanks a lot
A pleasure :smile:.
 

1. What is reactance?

Reactance is the opposition to the flow of alternating current (AC) caused by capacitance or inductance. It is measured in ohms and is represented by the symbol X.

2. How does reactance affect frequency?

Reactance is directly proportional to frequency. This means that as frequency increases, reactance also increases. Conversely, as frequency decreases, reactance decreases.

3. What is the significance of reactance being zero?

When reactance is zero, it means that there is no opposition to the flow of current. This occurs at a specific frequency known as the resonant frequency, where the capacitive and inductive reactance cancel each other out.

4. How is zero reactance used in practical applications?

Zero reactance is used in practical applications to achieve maximum efficiency in electronic circuits. For example, in a filter circuit, zero reactance can be used to block unwanted frequencies and only allow the desired frequency to pass through.

5. Can reactance ever be negative?

No, reactance cannot be negative. It is always a positive value, representing the opposition to current flow. However, it can be represented as a negative value in calculations when it is acting in opposition to another form of reactance.

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