Solve Freq of Coupled LC Circuit with Inductor

In summary, the problem at hand involves finding the normal frequencies of a coupled LC circuit, where the coupling is done by an inductor instead of a capacitor. The given equations for an LC circuit coupled by a capacitor are L(d2q1/dt2)+(1/C)q1+(1/C')(q1+q2)=0 and L(d2q2/dt2)+(1/C)q2+(1/C')(q1+q2)=0, but since the circuit in question is coupled by an inductor, these equations need to be modified. The current flowing through the inductor means that the equation I1 + I2 = 0 is no longer valid. The image provided shows an L' that is
  • #1
aseylys
22
0

Homework Statement



I have to find the normal frequencies of a coupled LC circuit. However, this LC circuit is coupled by an inductor, not a capacitor.
__|C|________|C|__
|...|...|
^I(1)...|...^I(2)
|...|...|
{L}...{L'}...{L}
|...|...|
|...|...|
--------------------

I'm sorry, I didn't have a picture but that's basically the circuit.

Homework Equations



I1+I2=0
I=dq/dt

These equations are for an LC circuit coupled by a capacitor:
L(d2q1/dt2)+(1/C)q1+(1/C')(q1+q2)=0

L(d2q2/dt2)+(1/C)q2+(1/C')(q1+q2)=0

The Attempt at a Solution



The only attempt I could figure out that it would be similar to that of a circuit coupled by a capacitor. I don't know if I'm on the right track or not and if I am I'm not sure how to modify the two equations.
 
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  • #2
I1 + I2 = 0 is no longer correct. Current flows through the inductor.
 
  • #3
I see an L' in your image but not in your equations. Conversely I see a C' in your equations but not in your image.
 

1. What is a coupled LC circuit with inductor?

A coupled LC circuit with inductor is a circuit that consists of two LC circuits connected together through an inductor. This inductor allows the two circuits to interact with each other, leading to oscillations and resonance.

2. How do you solve for the frequency of a coupled LC circuit?

To solve for the frequency of a coupled LC circuit, we use the equation f = 1 / (2π√(LC)), where f is the frequency, L is the inductance of the circuit, and C is the capacitance of the circuit.

3. What factors affect the frequency of a coupled LC circuit?

The frequency of a coupled LC circuit is affected by the values of the inductance and capacitance in the circuit. It is also influenced by external factors such as the resistance of the circuit and the quality of the components used.

4. How does changing the inductance and capacitance affect the frequency of a coupled LC circuit?

Increasing the inductance or capacitance in a coupled LC circuit will decrease the frequency. Conversely, decreasing the inductance or capacitance will increase the frequency. This is because the frequency is inversely proportional to the square root of the product of the inductance and capacitance.

5. Can a coupled LC circuit have multiple resonant frequencies?

Yes, a coupled LC circuit can have multiple resonant frequencies depending on the values of the inductance and capacitance. These resonant frequencies can be found by solving for the frequencies using the equation mentioned in question 2.

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