Leq = (L1*L2-M^2)/(L1*L2-M^2)Hope this helps

[gneill]

I think we're losing the plot a bit here. Your goal is to find expressions for $I_1$ and $I_2$ starting with the equations

$U = L_1 I_1 + M I_2~~~~~~~$ (1)
$U = L_2 I_2 + M I_1~~~~~~~$ (2)

Two equations in two unknowns. Everything else is treated as known constants. This is a typical pair of simultaneous equations which you wish to solve for the variables $I_1$ and $I_2$.

These equations have been solved in this thread already (granted the thread is getting rather large due to it being continuously "reawakened" by students with the same question and issues...), so I'm able to recap here without really giving anything away that hasn't already been presented.

Isolate $I_1$ equation (1):

$I_1 = \frac{(U - M I_2)}{L_1}$

Plug that expression for $I_1$ into equation (2):

$U = L_2 I_2 + M \frac{(U - M I_2)}{L_1}$

Solve for $I_2$:

$I_2 = \frac{L_1 - M}{L_1 L_2 - M^2}$

Now you have an expression for $I_2$ that only involves the known values.

Do a similar thing to find the expression for $I_1$, or use this $I_2$ result in equation (1) to eliminate $I_2$ there and solve for $I_1$, or simply look at the symmetry of the two equations and write the result for $I_2$ by inspection from the result for $I_2$.

 

[cablecutter]

okay so from

U = L1i1+M((L1-M)/(L1L2-M²))

L1i1 = U-M ((L1-M)/(L1L2-M²)

i1 = (U-M((L1-M)/(L1L2-M²)))/L1

Thanks for your Help gneill

 

[osykeo]

on part c i follow it up to solving for i2 but what i can't understand is how the U has been dropped;

by my workings i get:

I2= (U(L1-M)/L2L1-M^2)

where as the final for your i2 has dropped the U ?

am i missing something obvious here, seems to happen when youve be staring at a question for so long.

 

[Jason-Li]

on part c i follow it up to solving for i2 but what i can't understand is how the U has been dropped;

by my workings i get:

I2= (U(L1-M)/L2L1-M^2)

where as the final for your i2 has dropped the U ?

am i missing something obvious here, seems to happen when youve be staring at a question for so long.

I think we're losing the plot a bit here. Your goal is to find expressions for $I_1$ and $I_2$ starting with the equations

$U = L_1 I_1 + M I_2~~~~~~~$ (1)
$U = L_2 I_2 + M I_1~~~~~~~$ (2)

Two equations in two unknowns. Everything else is treated as known constants. This is a typical pair of simultaneous equations which you wish to solve for the variables $I_1$ and $I_2$.

These equations have been solved in this thread already (granted the thread is getting rather large due to it being continuously "reawakened" by students with the same question and issues...), so I'm able to recap here without really giving anything away that hasn't already been presented.

Isolate $I_1$ equation (1):

$I_1 = \frac{(U - M I_2)}{L_1}$

Plug that expression for $I_1$ into equation (2):

$U = L_2 I_2 + M \frac{(U - M I_2)}{L_1}$

Solve for $I_2$:

$I_2 = \frac{L_1 - M}{L_1 L_2 - M^2}$

Now you have an expression for $I_2$ that only involves the known values.

Do a similar thing to find the expression for $I_1$, or use this $I_2$ result in equation (1) to eliminate $I_2$ there and solve for $I_1$, or simply look at the symmetry of the two equations and write the result for $I_2$ by inspection from the result for $I_2$.

osykeo, I have the exact same query, although I think I have got the answer. You have to do it as follows:

I1=(U(L2-M))/(L1*L2-M^2)
I2=(U(L1-M))/(L1*L2-M^2)
Hence:
U=Leq (I1+I2)
U = Leq (U(L2-M))/(L1*L2-M^2)+(U(L1-M))/(L1*L2-M^2)

U = Leq ((UL1+UL2-2MU)/(L1*L2-M^2)

Then rearrange this for Leq