# Homework Help: Parallel Mutual Inductances

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1. Mar 5, 2018

### cablecutter

I'm unsure do i need to try and rearrange U=L2i2+M((U-Mi2)/L1
for i2?

or the original simultaneous equation (2) for i2?....
U = L2i2+Mi1
U-Mi1 = L2i2+Mi1-(Mi1)
(U-Mi1)/L2 = (L2i2)/L2
(U-(Mi1)/L2 = i2

2. Mar 5, 2018

Yes.

3. Mar 6, 2018

### cablecutter

so from U = L2i2+M(U-(Mi2))/L1

UL1 = L1L2i2+MU-M²i2

UL1-MU = L1L2i2-M²i2

UL1-MU = i2(L1L2-M²)

i2 = (UL1-MU)/(L1L2-M²)

am i right so far ?

4. Mar 6, 2018

Looks fine.

5. Mar 6, 2018

### cablecutter

UL1 = L1L2i2+MU-M²i2

UL1-MU = L1L2i2-M²i2

UL1-MU = i2(L1L2-M²)

i2 = (UL1-MU)/(L1L2-M²)

am i right so far ?[/QUOTE]

now replace i2 in equation (1) with above? do i replace both i2 and i1 in equation 1 or just i2?
can end up with:

U = L1i1+M((UL1-MU)/(L1L2-M²))

or

U = L1(U-(M((UL1-MU)/(L1L2-M²))/L1) + M((UL1-MU)/(L1L2-M²)) ?

you can then minus the L1 to give

U = U-(M((UL1-MU)/(L1L2-M²)) + M((UL1-MU)/(L1L2-M²)) which will end up canceling out to 0=0?

Last edited: Mar 6, 2018
6. Mar 6, 2018

### Staff: Mentor

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 $I_2$.

Last edited: Mar 6, 2018
7. Mar 8, 2018

### 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

8. Jun 18, 2018

### osykeo

on part c i follow it up to solving for i2 but what i cant 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.