AC Homework: 10 Ohms Resistor, 12 uF Capacitor, 28 mH Inductor

Click For Summary

Discussion Overview

The discussion revolves around a homework problem involving an AC circuit with a 10 ohm resistor, a 12 microFarad capacitor, and a 28 mH inductor connected in series with a 170 V generator. Participants are attempting to determine the frequency at which the rms current is maximum and the maximum value of the rms current.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant states they know how to solve for the frequency but encounters an issue with calculating the rms current, suggesting their answer of 3.52 A is incorrect compared to a stated value of 17 A.
  • Another participant requests clarification on how the 3.52 A was calculated to understand the error.
  • It is pointed out that the formula used for calculating rms current is incorrect as it does not account for the capacitor, and the impedance should include all components: Z = R + jωL + 1/(jωC).
  • A participant expresses confusion about whether their professor's guidance was incorrect, indicating a lack of clarity on the correct formula.
  • Further clarification is provided on the impedance formula, emphasizing the need to find the absolute value of Z and noting that the minimum impedance occurs when the reactances of L and C cancel each other out.
  • A hint is given that at the resonant frequency, the reactance is zero, which simplifies the calculation of current.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct approach to calculating the rms current, with multiple viewpoints on the formulas and methods to be used. Disagreement exists regarding the validity of the initial formula provided by the professor.

Contextual Notes

Participants express uncertainty regarding the application of formulas and the role of each component in the circuit's impedance. There are unresolved mathematical steps and assumptions about the circuit's behavior at resonance.

Ris Valdez
Messages
9
Reaction score
0

Homework Statement



A 10 ohms resistor, a 12 microFarad capacitor and a 28 mH inductor are connected in series with a 170 V generator. A.) At what frequency is the rms current maximum? B.) What is the maximum value of the rms current?

Homework Equations



A.) Fo = 1 / 2pi sqrtLC
b.) Irms = Vrms / 2pi fL

The Attempt at a Solution


This is a lecture thag I'm trying to study. I know how to get for A. But when I try inputting the variables, i get the wrong answer for B. It says its 17A. I've been getting 3.52. Can somebody help me please?
 
Physics news on Phys.org
Please show how you got 3.52 A, otherwise it is hard to understand what went wrong.
 
Ris Valdez said:
b.) Irms = Vrms / 2pi fL
That's not correct ( the capacitor is not included ).

The impedance: Z = R + jωL + 1/(jωC).
( ω = 2πf )

I = V / Z
 
mfb said:
Please show how you got 3.52 A, otherwise it is hard to understand what went wrong.
Using the formuka for B
Irms = Vrms / 2pi fL
= 170V / 2pi (274.57Hz) (28×10^-3H)
 
Hesch said:
That's not correct ( the capacitor is not included ).

The impedance: Z = R + jωL + 1/(jωC).
( ω = 2πf )

I = V / Z
So my professor was wrong? :0
 
Ris Valdez said:
So my professor was wrong? :0

I don't know what your professor has told you. :)
 
Hesch said:
I don't know what your professor has told you. :)
Hahaha
that's what she used in that number though. Can you tell me what's wrong with the formula and how to really use the right one? I'm really sorry for asking much but I'm quite stuck...
 
Hesch said:
The impedance: Z = R + jωL + 1/(jωC).
Well, The "formula" as for Z is the right one.

To find the current, you must find the absolute value for Z.

1/(jωC) = -j/(ωC) →
Z = R + j(ωL - 1/(ωC) )

Obvious the minimum value for |Z| is found when (ωL - 1/(ωC)) = 0. You have already found ω0 in (A), where (ω0L - 1/(ω0C)) = 0.

So |Z|min = R + j(ω0L - 1/(ω0C) ) = R →

Imax = V / R
 
Ris Valdez said:
Hahaha
that's what she used in that number though. Can you tell me what's wrong with the formula and how to really use the right one? I'm really sorry for asking much but I'm quite stuck...
Hint: at f = f0 there is no reactance, meaning L and C reactances cancel each other out. What's left?
 

Similar threads

  • · Replies 2 ·
Replies
2
Views
4K
  • · Replies 18 ·
Replies
18
Views
4K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 5 ·
Replies
5
Views
8K
  • · Replies 3 ·
Replies
3
Views
5K
  • · Replies 13 ·
Replies
13
Views
3K
  • · Replies 10 ·
Replies
10
Views
3K
  • · Replies 5 ·
Replies
5
Views
14K