# Magnetically coupled circuit problems

#### farmd684

Joined Jan 20, 2009
9 In this circuit i have got the following mesh equations :

mesh 1:

jI1+6jI2=12

mesh 2:

(j10+5-j4)I2+j4I1+2jI1=0

But in the book there is no j4 present. Why is that ?? I have tried without the -j4 term and the answer is right
otherwise its wrong. Here is mesh 1:

(20+j10)I1-j5I2=60<30

mesh 2:

( j20+j10)I2-j5I1-j10I1=0

but here in mesh2 why is the term (-2*j5)I2 is missing as i can see the current I2 is in series with them. MEsh 1 is :

(20+j10)I1-10jI2+j5I2=0 [i have done]

(j10+j20-10j)I1+j5I2=0 [by book]

how comes the (-j5*2) comes as current I1 is not series with those inductors

MEsh 2 :

(j20+j10)I2-j10I1+j5I1-(2*j5)I2=1

but the book left the term (-2*j5)I2 but why ??

Thanks

#### t_n_k

Joined Mar 6, 2009
5,447
Both your mesh equations for the first (top) circuit look correct to me.

I don't agree with your mesh 2 equation for the second (middle) circuit.

Haven't checked the third circuit.

I find an important step in solving mutually coupled circuits is to redraw the circuit with each of the mutually induced voltage components shown as an equivalent source with the appropriate magnitude and polarity. What approach do you take?

Since this is homework I'd suggest you might show some intermediate steps in your solution method so that forum members might be able to better understand where you are possibly going wrong.

#### farmd684

Joined Jan 20, 2009
9
Both your mesh equations for the first (top) circuit look correct to me.

I don't agree with your mesh 2 equation for the second (middle) circuit.

Haven't checked the third circuit.

I find an important step in solving mutually coupled circuits is to redraw the circuit with each of the mutually induced voltage components shown as an equivalent source with the appropriate magnitude and polarity. What approach do you take?

Since this is homework I'd suggest you might show some intermediate steps in your solution method so that forum members might be able to better understand where you are possibly going wrong.
could you please point me out what is the mistake i have made

I have used the dot method to get the signs of the circuit. This is not a homework problem and i have showed the difference between my workings and the book i want to know why i m wrong.

Thanks

#### t_n_k

Joined Mar 6, 2009
5,447
I agree with both of your derived mesh equations for the third problem. The book solution may well be incorrect.

In the second problem, keep in mind that both I1 & I2 flow in the j10 side of the mutually coupled coils. So the magnitude of the mutually induced voltage in the j20 coil due to the flow (I1-I2) in the j10 coil side will be 5j*(I1-I2). This voltage will oppose the indicated I2 current flow. The mutually induced voltage magnitude in the j10 side due to the flow of I2 in the j20 side will be 5j*I2. This voltage will aid the indicated I2 flow.

You seem to have taken the I1 & I2 contra-flow issue into account in the third example and come up with what I believe are the correct equations.

It would have helped if you had collected all the common terms in your mesh equations to give single coefficients of I1 & I2 in each of the equations.

#### farmd684

Joined Jan 20, 2009
9

the 2nd prob mesh 2 equation i have found this (after correction) :

(j20+j10)I2-j10I1=j5I1-(2*j5)I2=0

which after simplifying gives me like this

-j5I1+j20I2=0

is there anyway i can get the exact solution of my problem ? May be a computer analysis is a good idea. Well i still have to learn how to do this.

Thanks

#### t_n_k

Joined Mar 6, 2009
5,447

the 2nd prob mesh 2 equation i have found this (after correction) :

(j20+j10)I2-j10I1=j5I1-(2*j5)I2=0

which after simplifying gives me like this

-j5I1+j20I2=0
Looks good.

is there anyway i can get the exact solution of my problem ? May be a computer analysis is a good idea. Well i still have to learn how to do this.
Unfortunately I don't believe there is any software that follows the particular process of forming the correct (mesh or nodal) equations as an intermediate step. One can certainly use simulation (Spice based) software to come up with time based values of voltage and current for a given circuit layout. The problem in simulating the examples you have posted is that you must firstly translate the circuit back into the time domain, which means selecting a source frequency and then calculating the equivalent component values - I guess you can always set the source angular frequency to unity and the L & C values are then fairly easy to derive. Also since the Spice solution normally includes a transient part you then have to run the simulation for sufficiently long enough time for the parameters to have reached their steady-state values.

In the long run it's probably a matter of doing enough example problems to gain the necessary confidence in your ability to solve a previously unseen example. The magnetically coupled circuits you are working with probably cause the most "grief" for students in terms of acquiring that confidence - particularly with handling the dot convention and so forth.

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#### farmd684

Joined Jan 20, 2009
9
Thanks a lot for your help I have another question that in the first 1st figure i have got all the mesh currents and i m asked to get the energy stored at 15ms time. i can get the energy by using dot convention. Should i use -Mi1i2 or +Mi1i2 while calculating the stored energy ?

I can see both the current enters ar dotted terminals thus i should use +ve sign before Mi1i2 but the book says the opposite. Why is that ?

Thanks

• riditanisha