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

[Ris Valdez]

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?

 

[mfb]

Please show how you got 3.52 A, otherwise it is hard to understand what went wrong.

 

[Hesch]

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

 

[Ris Valdez]

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)

 

[Ris Valdez]

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

 

[Hesch]

So my professor was wrong? :0

I don't know what your professor has told you. :)

 

[Ris Valdez]

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]

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 →

I_max = V / R

 

[rude man]

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?