Find the impedance and ω for (R and L in series, & C in || )

In summary, the conversation discussed finding the impedance (Z) of a circuit with R and L in series, and C in parallel with them. It was mentioned that a circuit is in resonance if Z is real, and the task was to find ω in terms of R, L, and C in order to achieve this. The suggested solution involved finding Z, putting it in terms of x+iy, setting y=0 to find ω, and using j instead of i for imaginary numbers in circuit analysis.
  • #1
notnerd
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Homework Statement


Find the impedance (Z) of the circuit in the shown figure (R and L in series, and C in parallel with them). A circuit is said to be in resonance if Z is real, find ω in terms of R, L, and C?
upload_2016-10-2_12-56-13.png


Homework Equations


VR= RIeiωt
VL= LiωIeiωt
VC= (Ieiωt)/(iωc)

What I mean by I is I (not) H didn't know how to write it and i imaginary number, I hope the I wrote the equations clearly.

The Attempt at a Solution


What I think about is:
1. Find Z.
2. Put Z in term of x+iy.
3. If Z is real then y=0.
4. find ω from y=0.

If that correct I should find Z, but I'm not sure about it.
first I found Zseries for R & L = R+iωL
then Z = Zseries || ZC
Am I right? or there are some specific formulas as if all R, L & C are in series?
 
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  • #2
notnerd said:
first I found Zseries for R & L = R+iωL
then Z = Zseries || ZC
Am I right?
Yes.
notnerd said:
2. Put Z in term of x+iy.
3. If Z is real then y=0.
4. find ω from y=0.
Right.
 
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  • #3
notnerd said:
What I mean by I is I (not) H didn't know how to write it and i imaginary number, I hope the I wrote the equations clearly.
To avoid confusion with current, imaginary number 'i' in mathematics is denoted by 'j' in electrical circuit analysis. So the reactances become jXL and -jXc (Note 1/j= -j).
 
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Related to Find the impedance and ω for (R and L in series, & C in || )

1. What is impedance and how is it related to R, L, and C?

Impedance is a measure of the opposition a circuit presents to the flow of current. It is affected by the values of resistance (R), inductance (L), and capacitance (C) in a circuit. In a series circuit, impedance is the sum of the individual impedance values of R and L. In a parallel circuit, impedance is the inverse of the sum of the individual inverse impedance values of C.

2. How do you find the impedance for R and L in series?

To find the impedance for R and L in series, you can use the formula Z = √(R^2 + (ωL)^2), where Z is the impedance, R is the resistance, ω is the angular frequency, and L is the inductance. This formula takes into account the resistance and inductive reactance (ωL) in the circuit.

3. How do you find the impedance for C in parallel?

To find the impedance for C in parallel, you can use the formula Z = 1/√(1/R^2 + (1/(ωC))^2), where Z is the impedance, R is the resistance, ω is the angular frequency, and C is the capacitance. This formula takes into account the resistance and capacitive reactance (1/(ωC)) in the circuit.

4. What is the significance of ω in the formulas for impedance?

ω (omega) is the angular frequency, which is a measure of how quickly a circuit is alternating between positive and negative values. It is related to the frequency (f) of the circuit through the formula ω = 2πf. ω is important in the formulas for impedance because it affects the overall value of the impedance in a circuit.

5. Can you provide an example of finding the impedance for R and L in series and C in parallel?

Yes, for example, let's say we have a circuit with a resistor (R = 10 ohms) and an inductor (L = 0.05 henries) in series, and a capacitor (C = 0.001 farads) in parallel. The angular frequency of the circuit is ω = 100 radians/second. To find the impedance for R and L in series, we use the formula Z = √(R^2 + (ωL)^2), so Z = √(10^2 + (100*0.05)^2) = √(10^2 + 25) = √125 = 11.18 ohms. To find the impedance for C in parallel, we use the formula Z = 1/√(1/R^2 + (1/(ωC))^2), so Z = 1/√(1/10^2 + (1/(100*0.001))^2) = 1/√(0.01 + 10^4) = 1/√10000.01 = 0.01 ohms.

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