Can You Solve This Circuit with Mutual Inductance and Capacitance?

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Homework Help Overview

The discussion revolves around a circuit problem involving mutual inductance and capacitance, where the original poster seeks to derive functions for current based on given equations that incorporate mutual inductance.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster formulates two equations related to the circuit, questioning their validity and seeking guidance on the next steps. Participants inquire about the meaning of the variable Q and its relationship to the currents I1 and I2, suggesting that a third equation is necessary for a complete solution.

Discussion Status

The discussion is ongoing, with participants exploring the relationships between the variables involved. Some guidance has been offered regarding the need for an additional equation to solve for the three variables present, but no consensus has been reached on the specific form of this equation.

Contextual Notes

Participants note that the original equations contain three variables (Q, I1, I2) but only two equations, indicating a need for further information or assumptions to progress.

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Homework Statement



In the given picture, I need to formulate some kind of solution to find functions for the current, knowing that the two inductances create a mutual inductance (coupling)

The Attempt at a Solution



I start by formulating these two equations where M is the mutual inductance.

For the left, E= Q/C + L1*dI1/dt - M*dI2/dt
and
for the right, 0= L2*dI2/dt + R*I2 - M*dI1/dt

Does this look okay so far, and where should I go from here?
 

Attachments

  • circuit 1.jpg
    circuit 1.jpg
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What is Q?. Find it and the question will be solved.
 
Q is just the charge on the capacitor
 
Is there a relation between Q and I1, I2 ?
 
I'm sure there is one, but Q is just a characteristic of the capacitor.
 
Slightly said:
I'm sure there is one, but Q is just a characteristic of the capacitor.

The two equations you have made have 3 variables(Q ,I1, I2,) so it can't be solved. Try to get a third equation and you will have 3 equations for three variables.

Hint: The third equation is a relation between I1 and Q. What is it?
 

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