Finding the impedance of circuits.

In summary, The conversation is about a junior circuits lab that expects familiarity with impedance but the intro E/M course did not cover it. The person is asking for confirmation on two impedance problems and also for help with plotting the phase of Z1 as a function of frequency. The summary also mentions a caution to retain the signs when computing arc tan and a correction made by the person. They also mention that the quadrant is not an issue since they are plotting the phase over a large frequency range. Finally, the person draws attention to a mistake and it is corrected.
  • #1
RobLikesBrunc
29
0
I'm currently taking a junior circuits lab that expects familiarity with impedance (my intro E/M course never covered it), so I just want to make sure I did these two impedance problems correctly (the second one asks merely for a formula, so no calculation was done):

tFqniA0.png


t5RyQE3.png


Later in the assignment, I'm also asked the plot the phase of Z1 as a function of frequency. For that (letting Z1 = x + yi), the phase is just arctan(y/x), right?

Thanks.
 
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  • #2
Seems all good to me.
 
  • #3
RobLikesBrunc said:
Later in the assignment, I'm also asked the plot the phase of Z1 as a function of frequency. For that (letting Z1 = x + yi), the phase is just arctan(y/x), right?

Thanks.

Looks good to me also.

Caution: in computing arc tan (y/x), be sure to retain the signs of x and y to determine in which quadrant the angle belongs. Arc tan b/(-a) is not the same angle as arc tan (-b)/a.
 
  • #4
rude man said:
Looks good to me also.

Caution: in computing arc tan (y/x), be sure to retain the signs of x and y to determine in which quadrant the angle belongs. Arc tan b/(-a) is not the same angle as arc tan (-b)/a.

There was actually a little mistake--on the last line I replaced the -i with -1 :P

Anyway, I was actually plotting the phase over 10^6 frequency range, so which quadrant to place it in is a non-issue. It looks pretty neat too (note the x-axis is logarithmic):

4RHtjSy.png
 
  • #5
Whoops, messed up a sign. Should be this:

yD2t7Ia.png
 
  • #6
RobLikesBrunc said:
Whoops, messed up a sign. Should be this:

yD2t7Ia.png

I was a about to draw your attention to that! Now it's OK.
 

FAQ: Finding the impedance of circuits.

1. How is impedance different from resistance?

Impedance is a measure of the total opposition to current flow in a circuit, taking into account both resistance and reactance. Resistance only considers the opposition caused by resistors.

2. What units are used to measure impedance?

Impedance is measured in ohms, just like resistance.

3. How do I calculate impedance?

Impedance can be calculated by using the formula Z = R + jX, where Z is impedance, R is resistance, and X is reactance. Reactance is often found by using the equations for capacitive and inductive reactance, depending on the components in the circuit.

4. Can impedance be negative?

Yes, impedance can have a negative value. This typically occurs when the circuit contains a component with a negative reactance, such as a capacitor or inductor.

5. How does impedance affect the behavior of a circuit?

Impedance affects the flow of current in a circuit. Higher impedance means there is more opposition to current flow, resulting in less current being able to flow through the circuit. This can impact the performance and efficiency of the circuit.

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