Solving Impedance Diagrams: Finding i(t) with XL = ωL

In summary, the conversation discusses finding the current in a circuit using impedance and Ohm's law. The speaker initially calculates the inductive reactance (XL) and phase angle, but is corrected by another speaker. The correct method is then explained, which involves converting the inductance to an impedance and using Ohm's law to find the current.
  • #1
k31453
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Homework Statement



Homework Equations


impedence diagram, XL = ωL

The Attempt at a Solution



Ok i got XL = 47 ohm
Then my phase angle is 88.8 degree.

Then to find i(t) i have to add that angle to the function right?
 
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  • #2
Your question isnot visible. Can you write it?
 
  • #3
k31453 said:
Ok i got XL = 47 ohm
Then my phase angle is 88.8 degree.

That's not quite right.

If you show your work maybe we can help find where things went wrong.
 
  • #4
Convert the inductance to an impedance and add it to the resistance. You now have an equivalent circuit with the voltage drop across the impedance given. Use Ohm's law to find the current.

Remember ω = 2*pi*f
 
  • #5


Yes, you are correct. In order to find i(t), you will need to add the phase angle to the function. This is because the impedance diagram represents a phasor diagram, where the magnitude of the phasor is the impedance and the angle represents the phase difference between the voltage and current. By adding the phase angle to the function, you will be able to solve for i(t) and determine its magnitude and phase. Remember to also consider the frequency (ω) in your calculation, as it affects the value of the inductive reactance (XL). Keep up the good work in solving impedance diagrams!
 

FAQ: Solving Impedance Diagrams: Finding i(t) with XL = ωL

What is an impedance diagram?

An impedance diagram is a graphical representation of the impedance of a circuit as a function of frequency. It is a plot of the magnitude and phase of the impedance as the frequency changes.

How do I find i(t) in a circuit with XL = ωL?

To find i(t), you can use Ohm's Law (i(t) = V(t)/Z) where Z is the impedance of the circuit. In the case of XL = ωL, Z = jωL, where j is the imaginary unit and ω is the angular frequency. Once you have the value of Z, you can solve for i(t) using the voltage and the calculated impedance.

Can I use an impedance diagram for all types of circuits?

Yes, an impedance diagram can be used for all types of circuits, including AC circuits with resistors, capacitors, and inductors. It is particularly useful for analyzing circuits with reactive components, such as those with XL = ωL.

What is the significance of XL = ωL in an impedance diagram?

XL = ωL represents the reactance of an inductor in an AC circuit. It is equal to the product of the angular frequency (ω) and the inductance (L). This value is important in an impedance diagram because it shows the relationship between the frequency and the inductance in the circuit.

How can I use an impedance diagram to troubleshoot a circuit?

An impedance diagram can help you identify potential issues in a circuit by showing the changes in the impedance at different frequencies. If there is a sudden change in the impedance, it could indicate a problem with a component in the circuit. You can also compare the impedance diagram of a faulty circuit to that of a working circuit to pinpoint the issue.

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