Solving a Series LRC Circuit with Complex Impedances

In summary, the problem involves a series L-R-C circuit driven by an AC voltage with a specific amplitude and frequency. The goal is to find the ratio of Vout/Vin, which can be solved using Kirchhoff's voltage and loop rules. The dots in the circuit represent voltage measurement points, and the impedance of each component (inductor and capacitor) must be taken into account. The current in the circuit can be expressed in terms of the source voltage and impedances.
  • #1
nateja
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Homework Statement


A series L-R-C circuit consisting of a voltage source, a capacitor of capacitance , an inductor of inductance , and a resistor of resistance is driven with an AC voltage of amplitude and frequency . Define to be the amplitude of the voltage across the resistor and the inductor.

FIND THE ratio Vout/Vin

picture: http://www.chegg.com/homework-help/questions-and-answers/series-l-r-c-circuit-consisting-voltage-source-acapacitor-capacitance-inductor-inductance--q416667?frbt=1

Homework Equations



Z = sqrt((IR)^2+(I*X_L-I*X_C)^2)

The Attempt at a Solution



I found Vin = sqrt((IR)^2+(I*X_L-I*X_C)^2)

Then I googled the question for Vout and tried to use kirchhoffs voltage and loop rule. I only found solutions using laplace transforms or something - I am in calc 2.

Any kind of hint in the right direction would be nice. I don't understand the 'dot' notation on the circuit. And the whole problem is really throwing me in circles.
 
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  • #2
In a circuit, open circles are usually used to represent points (terminals) at which you measure a voltage. In this case, they've used closed circles instead, and they're just indicating that Vout is the voltage measured between these two terminals.

That's all the dots are.
 
  • #3
You don't need to use Laplace transforms. You can just use KVL and solve the circuit normally, except that you need to use the impedance of each component which, in general, is a complex number.

What is the expression for the impedance of an inductor? How about a capacitor?

Since this is a series circuit, what is the current in terms of the source voltage and the impedances?
 

1. What is an LRC circuit with odd notation?

An LRC circuit with odd notation is an electrical circuit that consists of an inductor (L), a resistor (R), and a capacitor (C) connected in series or parallel. The odd notation refers to the use of Greek letters to represent these components in the circuit diagram.

2. How does an LRC circuit with odd notation work?

An LRC circuit with odd notation works by storing energy in the form of electric and magnetic fields. The inductor stores energy in its magnetic field, the capacitor stores energy in its electric field, and the resistor dissipates energy in the form of heat. The interaction between these components creates a resonant frequency, which determines the behavior of the circuit.

3. What is the difference between series and parallel LRC circuits with odd notation?

In a series LRC circuit with odd notation, the components are connected end-to-end, so the current flowing through each component is the same. In a parallel LRC circuit, the components are connected side by side, so the voltage across each component is the same. The behavior and calculations for these two types of circuits are different.

4. How do I calculate the resonant frequency of an LRC circuit with odd notation?

The resonant frequency of an LRC circuit with odd notation can be calculated using the formula f = 1/(2π√(LC)), where f is the resonant frequency, L is the inductance in henries, and C is the capacitance in farads. This formula applies to both series and parallel LRC circuits.

5. What are some practical applications of LRC circuits with odd notation?

LRC circuits with odd notation have various practical applications, such as in radio and television receivers, electronic filters, and oscillators. They are also used in power supplies to regulate voltage and in electric motors to control speed. Additionally, LRC circuits are important in understanding the behavior of other more complex circuits and systems.

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