What is V(K) of inductor given coupling coefficent?

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    Coupling Inductor
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Discussion Overview

The discussion revolves around determining the voltage across an inductor given the coupling coefficient and the currents in a circuit involving multiple inductors. The scope includes theoretical analysis and application of mesh current equations in electrical engineering.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant expresses difficulty in solving mesh current equations for the circuit involving inductors, indicating a reliance on guesses for the answer.
  • Another participant suggests writing down the equation for the voltage drop across one of the inductors, emphasizing the need to consider the currents involved.
  • Participants discuss the application of mesh equations, with one noting the typical voltage drop across an inductor and questioning how mutual inductance affects this relationship.
  • There is a proposal that the voltage drop could be expressed as a function of the currents in both inductors, incorporating mutual inductance, with a specific equation suggested based on a reference from a book.
  • One participant confirms the correctness of a proposed equation related to the voltage drop across the inductor.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the correct application of mesh equations and the influence of mutual inductance on the voltage drop across the inductor. There is no clear consensus on the correct formulation of the voltage drop, and multiple approaches are discussed.

Contextual Notes

Participants mention specific values for inductance and coupling coefficient but do not resolve the implications of these values on the equations presented. The discussion includes assumptions about the arrangement of inductors and the influence of mutual inductance, which remain unresolved.

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Homework Statement


ri87wh.jpg



Homework Equations


k=1
inductor(left)=400j
inductor(right)=1600j


The Attempt at a Solution



how to do this! help me. my caluclator can't solve 3 rectangular form mesh currents equations so i cannot solve for individual currents for all 3 loops! i just guessed on this answer. i put 400j(I1)-(1600+400)j(I2) or D.

A. -j400 I1+j1600 I2 (A)
B. j400 I1+j400 I2 (A)
C. -j400 I1-j400 I2 (A)
D. j400 I1-j1200 I2 (A)
 
Last edited:
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Not my choice.

Write down the equation for voltage drop across L1 (jX = j400) due to one or more of i1, i2 and i3.
 
ok using mesh equations?
-20+3I1+j400(I1-I2)=0
(3+j400)I1-(j400)I2=20 (for mesh 1)

don't know if I'm doing this right. I know usually V1=M*di2/dt for mutual inductors especially with this arrangement of dots but not sure how to apply that. voltage drop normally across the inductor would be Vk=j400(I1-I2) but not sure with this arrangement.
 
Last edited:
asdf12312 said:
ok using mesh equations?
-20+3I1+j400(I1-I2)=0
(3+j400)I1-(j400)I2=20 (for mesh 1)

don't know if I'm doing this right. I know usually V1=M*di2/dt for mutual inductors especially with this arrangement of dots but not sure how to apply that. voltage drop normally across the inductor would be Vk=j400(I1-I2) but not sure with this arrangement.

Without mutual inductance Vk=j400(I1-I2) would be correct, but there is mutual inductance M.

The voltage drop across L1 is due to the current in L1 and the current in L2. What is the current in L2 and how does it affect the voltage across L1?

The voltage sources will not appear in your equation. You are dealing with the currents i1, i2 and/or i3 only.
 
I am guessing its jw(L1(I1-I2)+M(I2)) based on a similar equation in my book. Would this be right? M I got as k*sqrt(L1*L2)=8. So j400I1+j400I2?
 
asdf12312 said:
I am guessing its jw(L1(I1-I2)+M(I2)) based on a similar equation in my book. Would this be right? M I got as k*sqrt(L1*L2)=8. So j400I1+j400I2?

Ah, yes, straight A!
 

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