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The penny has dropped, L minus 0.25xL leaves three quarters of an L!gneill said:You just need to practice your algebra.
Continue. Factor out the L on the right hand side.
i.e. 0.75L
Thank you gneill.
The penny has dropped, L minus 0.25xL leaves three quarters of an L!gneill said:You just need to practice your algebra.
Continue. Factor out the L on the right hand side.
Good Morninggneill said:Can't do much about the algebra getting messy other than organize the symbols better. To unclutter things a bit let E = V/JW.
Your two equations are then:
E=L1i1 + Mi2 (1)
E=L2i2 + Mi1 (2)
##ω## is the angular frequency of the voltage source V which is presumed to be an AC sinusoidal source. ##j## is the square root of negative one, that is, ##j = \sqrt{-1}##. That makes ##jω## an imaginary value.David J said:Good Morning
I have started looking at this question now (part a) My notes tell me virtually nothing about this question so I am trying to get an understanding by looking through the posts of this thread. I have noticed the terminology jw used a lot but i could not work out what it was but then someone changed it to the latex form ##jw##. And now in this post it has been replaced by E, E being equivalent to ##\frac{v}{jw}## The E means more sense to me than##jw## but I was just wondering if someone could explain where ##jw## is derived from please?? Thanks
Hello, I am looking at this question and struggling to understand how ##I1## and ##I2## were obtained. Do calculators offer this function? Not necessarily to solve for ##I1## and ##I2## but to re arrange for ##I1## and ##I2## as is required here ??earthloop said:Yeah I have tried using the equations from a), but am struggling with solving them simultaneously.
V=jw*L1*I1+jw*M*I2
V=jw*L2*I2+jw*M*I1
I have input it into my calculator to solve for I1 and I2 and get the correct answers. I can't get the same answer in Wolfram. I would really like to know how to solve these two for I1 and I2 without using my calculator. Any more help would be hugely appreciated. Maybe just the first step to solving, to get the ball rolling?
Thanks
At this point you should be able to find the ratio I1/I2 with a bit of algebra on the last expression. Just gather the I1 terms on one side and the I2 terms on the other...ShortCircuit said:First of I have the equations from question A)
ABEF : V= jw*L1*I1+jw*M*I2
ABCDEF : V=jw*L2*I2+jw*M*I1
Now on to question B)
V=V
jw*L1*I1+jw*M*I2 = jw*L2*I2+jw*M*I1
Factorise jw
jw(L1*I1+M*I2) = jw(L2*I2+M*I1)
Divide by JW
L1*I1+M*I2 = L2*I2+M*I1
M is the mutual inductance that links the two inductors.Student12345 said:Hi I'm just starting this question and and maybe this is a little stupid but what does M represent in this circuit? At first I assumed both L1and L2 had an inductance of M but it can't be. Is it XL?
gneill said:This gets you as far as a relationship between i1 and i2, but doesn't address the equivalent inductance since it doesn't relate the total current to the driving voltage.
There's only one voltage here, V the source voltage. If you could find an expression for V/I , where I is the total source current, then you would have the impedance of the load.
Here's a starting point I can suggest. Use KVL and write two loop equations per:
View attachment 109129
Handle the mutual inductances as required, of course. Two equations, two unknowns (##I_1## and ##I_2##). Solve for the two currents. The sum of the two currents is the total current, so that:
##\frac{V}{jωL_{eq}} = I_1 + I_2##
Yes.Triopas said:Thank you gneill.
Should I solve the second two equations for I1 and I2 as simultaneous equations?
Don't start by equating them; The resulting solutions for the ##I##'s should involve ##U##, ##L_1##, ##L_2##, and ##M##.##L_1 I_1 + M I_2 = L_2 I_2 + M I_1##
##\sqrt{-1} \cdot \omega##Spongecake said:I'm sure i am being silly but what does Jw stand for?
Yeah, looks like something's gone wrong with your algebra. Try again, perhaps showing us your work step-by step.cablecutter said:i2= ((U-M)/L2) +M((U-M)/L1) ? i have a feeling its way out.
Yes.cablecutter said:I'm unsure do i need to try and rearrange U=L2i2+M((U-Mi2)/L1
for i2?