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

In summary, the conversation discusses a problem involving a series circuit with a resistor, capacitor, inductor, and generator. The question is asked about the frequency at which the maximum rms current occurs and what the maximum value of the rms current is. The conversation also mentions the formula for calculating the rms current and the impedance, as well as a discrepancy in the answer obtained for the maximum current. The expert suggests using the concept of reactance to find the correct answer, as at the resonant frequency the reactances of the inductor and capacitor cancel each other out, leaving only the resistance.
  • #1
Ris Valdez
9
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?
 
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  • #2
Please show how you got 3.52 A, otherwise it is hard to understand what went wrong.
 
  • #3
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
 
  • #4
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)
 
  • #5
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
 
  • #6
Ris Valdez said:
So my professor was wrong? :0

I don't know what your professor has told you. :)
 
  • #7
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...
 
  • #8
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
 
  • #9
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?
 

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

1. What is the purpose of using a 10 Ohms resistor, 12 uF capacitor, and 28 mH inductor in AC homework?

The purpose of using these components in AC homework is to demonstrate the behavior and characteristics of circuits with resistors, capacitors, and inductors when exposed to alternating current (AC) electricity.

2. What is the significance of the values 10 Ohms, 12 uF, and 28 mH in this homework?

The values of 10 Ohms, 12 uF, and 28 mH were likely chosen to create a circuit with specific parameters for the purposes of analysis and experimentation.

3. Can you explain the function of a resistor, capacitor, and inductor in an AC circuit?

A resistor is used to limit the flow of electricity in a circuit, while a capacitor is used to store and release electrical energy. An inductor, on the other hand, is used to store and release magnetic energy. In an AC circuit, these components work together to regulate the flow of electricity and create specific behaviors within the circuit.

4. How do the values of the resistor, capacitor, and inductor affect the behavior of an AC circuit?

The values of these components can affect the frequency, voltage, and current of the AC circuit. For example, increasing the value of the inductor can decrease the frequency of the circuit, while increasing the value of the capacitor can increase the voltage.

5. What are some potential applications of circuits with resistors, capacitors, and inductors in an AC system?

Circuits with these components can be used in various electronic devices, such as filters, amplifiers, and oscillators. They are also commonly used in power grids and other AC systems for regulating and controlling electricity flow.

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