Minimize Impedance - (eletromagnetism)

Just remember to use the correct units for the values given (16k\ohm and 8.0\mu F) and the final answer (0.009kHz).In summary, the question asks for the frequency needed to minimize impedance in an RLC circuit with a resistance of 16k\ohm, a capacitance of 8.0\mu F, and an inductance of 38.0H. The minimum impedance is achieved at resonance, where the impedance is equal to the resistance (Z = R). By solving for the frequency (f = \frac{1}{2\pi\sqrt{LC}}), we can find that the frequency needed to minimize impedance is 0.009kHz.
  • #1
FrogPad
810
0
OK, I think I am doing this question right, but I'm not exactly sure. The question is as follows:

For an RLC circuit with a resistance of [tex]16k\ohm [/tex], a capacitance of [tex]8.0\mu F [/tex] and an inductance of [tex]38.0H[/tex] what frequency is needed to minimize the impedance?

Well impedance is give by:
[tex] Z = \sqrt{R^2 + (X_C - X_L)^2} [/tex]

Putting [tex] X_C [/tex] and [tex] X_L [/tex] in terms of [tex] L, C, \omega [/tex] we then have:

[tex] Z =\sqrt{R^2 + \left(\omega L - \frac{1}{\omega C}\right)^2} [/tex]
Minimum impedance is acheived at resonance, so [tex] Z = R [/tex]

Thus we have:
[tex] R =\sqrt{R^2 + \left(\omega L - \frac{1}{\omega C}\right)^2} [/tex]

Solving this for [tex] \omega [/tex] yields:

[tex] \omega = \frac{1}{\sqrt{LC}} [/tex]

And frequency is given by: [tex] f = \frac{\omega}{2\pi} [/tex]

So solving [tex] f [/tex] for [tex] \omega [/tex] and substituting into the equation above gives:

[tex] f 2\pi = \frac{1}{\sqrt{LC}} [/tex]

Now solving for [tex] f [/tex] yields:
[tex] f = \frac{1}{2\pi\sqrt{LC}} [/tex]

And finally plugging in [tex] L,\,C[/tex] from above gives:

[tex] f = \frac{1}{2\pi\sqrt{(38.0H)(8.0\mu F)}} = 9.12Hz = 0.009kHz[/tex]

So I'm pretty sure there are going to be a few questions like this on my test tomorrow, so I just want to make sure I'm doing this correctly. Thank you.
 
Physics news on Phys.org
  • #2
Looks good.
 
  • #3


Your calculation and approach seem correct. In order to minimize impedance, you need to find the frequency at which the reactance of the inductor and capacitor cancel each other out, leaving only the resistance. This is known as resonance. Your calculation for the resonant frequency, 9.12Hz, is correct. Just make sure to double check your units and calculations before your test tomorrow. Best of luck!
 

Related to Minimize Impedance - (eletromagnetism)

1. What is impedance and why is it important in electromagnetism?

Impedance is a measure of the opposition to the flow of alternating current in a circuit. In electromagnetism, impedance is important because it determines the strength of the electromagnetic field and the amount of energy that can be transferred through the circuit.

2. How can impedance be minimized in a circuit?

Impedance can be minimized by using conductive materials with low resistivity, minimizing the length and width of the circuit, and using components with low impedance values. Additionally, keeping the circuit isolated from external electromagnetic interference can also help minimize impedance.

3. What factors can affect impedance in a circuit?

The main factors that can affect impedance in a circuit are the type of material used, the length and width of the circuit, and the frequency of the alternating current. Other factors such as temperature and external electromagnetic interference can also play a role.

4. How does minimizing impedance improve the performance of electronic devices?

Minimizing impedance can improve the performance of electronic devices by reducing power losses and improving the efficiency of energy transfer. This can result in faster and more reliable operation of the device.

5. Are there any disadvantages to minimizing impedance in a circuit?

While minimizing impedance can have many benefits, there are some potential disadvantages to consider. For example, using materials with low resistivity can be expensive, and reducing the size of a circuit may make it more difficult to troubleshoot and repair. Additionally, minimizing impedance too much can also lead to unwanted electromagnetic interference and signal distortion.

Similar threads

  • Introductory Physics Homework Help
Replies
4
Views
342
  • Introductory Physics Homework Help
Replies
3
Views
323
  • Introductory Physics Homework Help
Replies
8
Views
387
  • Introductory Physics Homework Help
Replies
6
Views
108
Replies
3
Views
861
  • Introductory Physics Homework Help
Replies
6
Views
283
  • Introductory Physics Homework Help
Replies
3
Views
242
  • Introductory Physics Homework Help
Replies
2
Views
788
  • Introductory Physics Homework Help
Replies
14
Views
1K
  • Introductory Physics Homework Help
Replies
17
Views
583
Back
Top