Magnitude of voltage across impedance

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Discussion Overview

The discussion revolves around calculating the magnitude of voltage across various impedances in an AC circuit consisting of resistors, an inductor, and a capacitor. Participants explore the total impedance of the circuit and the resulting current, as well as the voltages across specific components.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant attempts to calculate the total impedance of the circuit by summing the resistances and reactances of the components.
  • Another participant emphasizes the need to treat capacitors and inductors as complex values, suggesting the use of complex notation for impedance.
  • A participant questions their total impedance calculation and arrives at a different value, prompting further clarification on how to combine real and imaginary components.
  • There is a correction regarding the total impedance, with a participant noting that it should be expressed in complex form, highlighting the importance of phase angles in AC circuits.
  • One participant expresses uncertainty about their calculations and acknowledges the complexity of the topic, indicating a need for further review.
  • Another participant provides updated calculations for total impedance and current, along with the magnitudes of the voltages across specific components.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the total impedance or the current calculations, as multiple competing views and corrections are presented throughout the discussion.

Contextual Notes

There are unresolved mathematical steps regarding the calculation of total impedance and the treatment of complex numbers. Participants express varying degrees of understanding of AC circuit principles, which may affect their calculations.

KK25
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Homework Statement



The following three impedances are connected in series across a 100-V, 20-kHz supply:
(1) a 12-Ω resistor, (2) a coil of 100 μH inductance and 5-Ω resistance and (3) a 390-nF
capacitor in series with a 15 Ω resistor. Sketch the circuit diagram, impedance diagram and the phasor diagram; take the supply voltage V as the reference phasor.

(a) Calculate the magnitude of the voltage V2 across the second impedance.

(b) Calculate the magnitude of the voltage V3 across the third impedance.2. The attempt at a solution

Ok, I'm pretty lost here, but this is what I have done so far...

I'm trying to get the current amount flowing in the circuit, so thought I should get a total impedance Z for the circuit.

First resistor = 12 Ohms
For the coil = 5 + 2 * Pi * (20*10^3) * (100*10^-6) = 17.6 Ohms
For the Capacitor = 1 / 2 * Pi * (20*10^3) * (390*10^-9) = 20.4 Ohms
Second resistor = 15 Ohms

Total Z for the circuit = 12+17.6+20.4+15 = 65 Ohms.

That is as far as I have gone so far. Is that the correct way to get total Z?

Next I will find the current by using I = V/Z ?

I guess that would be 1.54 A ?
 
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Keep in mind that capacitors and inductors are complex values.

X_l=j17.6 ohm
X_c=-j20.4 ohm

Total impedance is then Z=R+j(X_l-X_c)

Sketch up the impedance diagram(complex plane) and you see why.
 
Ok. I see that in this diagram:

[PLAIN]http://macao.communications.museum/images/exhibits/small/2_4_4_1_eng.png

Does that mean my total Z is in fact 24.2 Ohms?

I came to that conclusion by using 27 + (-2.8)

Sorry if I'm not getting it, I'm finding it hard to get my head around these AC basics :blushing:
 
Last edited by a moderator:
Nope. The total impedance is Z=27-j2.8

You can't sum real and imaginary numbers. Just like vectors, the impedance consist of an angle and magnitude.

Current is then: I=U/R=100+j0 / 27-j2.8=...A
 
I've come up with a figure of 3.69 A

How does that sound?

Thanks for posting back by the way :)
 
Wrong. It's supposed to be a complex number with both real and imaginary parts. (i.e I=2+j3 A or 3A <(angle) 36*)
Using a scientific calculator does this job easy, calculating by hand requires using complex conjugate. Refer to your calculus textbook.

Said in other words, the current has a phase angle in reference to the voltage source (leading or lagging current, Power factor and so forth)

BTW: I have to correct my answer Z=32 - j2.8 ohm
Didnt read the text thoroughly Total resistance is: 12 + 5 + 15 =32 ohm
But still, your current must have a phase angle.
 
Gah... Back to the drawing board.

Was working on other parts of my assignment today, I'll give this another shot tomorrow.

Thanks
 
Ok... Had another attempt.

Total Z = 32 - j7.8 (rather than 2.8 as before)

I = 3 A /_ -13.7

Magnitude of Voltage across coil = 40.8V

Magnitude of Voltage across both 15 Ohm resistor & Capacitor = 75.9V
 

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