So you'd use the top loop and the right-hand loop.

[Princess19]

Homework Statement

http://img251.imageshack.us/img251/3123/photo2152.jpg

Homework Equations

i don't know of any..

The Attempt at a Solution

Ok, so the professor told us to develop three equations, but to only use two of those to try and solve for the currents, i1, i2, i3.

All i know is the currents coming in are equal to the ones coming out.

So, I probably have these wrong, but here are the equations so far.

1) I2 + I3 = I1
2) -I3R3 - V2 - I1R1 + V1 = 0
3) -I3R3 - V2 - I1R1 + V1 = 0


are these wrong? help me get them right, I am so lost.

 

[tiny-tim]

Hi Princess19!

(try using the X₂ icon just above the Reply box )

Your 1) and 2) look right …

but you've copied your 3) wrong, it's the same as 2) !

btw, I think you've misunderstood your professor …

Ok, so the professor told us to develop three equations, but to only use two of those to try and solve for the currents, i1, i2, i3.

… this circuit has 2 loops, so you do need 3 equations to solve it: one junction and 2 loop equations

I think your professor meant that there are 3 loop equations (left loop right loop and outer loop), but you only need 2 of them (because they're linearly dependent), plus a junction loop, making 3 …

and he wants you to write all three loop equations, but then use only 2 of them

 

[Princess19]

oops! would this be equation 3?

i₃R₃ - i₂R₂ + V₂ = 0

 

[tiny-tim]

Hi Princess19!

oops! would this be equation 3?

i₃R₃ - i₂R₂ + V₂ = 0

he he!

Yes, that looks good …

now solve!​

(btw, you still haven't given the third loop equation. )

 

[Princess19]

is the first equation a loop equation?

i have no idea about the third loop equation. can you give me some sort of hint to get started on?

 

[tiny-tim]

The first equation is a junction equation (i'm not sure that's the official name, but it's what I call it ).

The 3rd loop equation is for the outside loop, ie the one with V₁ R₁ and R₂.

 

[Princess19]

would equation 3 be i3R3 - i2R2 + V2 = 0 or -i3R3 - i2R2 + V2 = 0


okay, how about this for the outer loop

V₁ - I₂R₂ - I₁R₁ = 0

 

[tiny-tim]

Hi Princess19!

(just got up :zzz: …)

would equation 3 be i3R3 - i2R2 + V2 = 0 or -i3R3 - i2R2 + V2 = 0

You're marking I₃ as going down the page, ie anti-clockwise in that loop, and I₂ as clockwise, so they must be opposites, so it's the first one (which you had originally, in post 3 ).

Personal grouch: I don't like professors who tell you to draw those circular arrows … I think it's much safer to draw arrows directly on the lines themselves … then you can easily see which currents are going the "wrong way" through any resistor, and how they add up at each junction.​

okay, how about this for the outer loop

V₁ - I₂R₂ - I₁R₁ = 0

Yes, that's right.

Note that this loop equation is the sum of the other two loop equations, so it gives no new information …

that's what your professor meant about only needing to use two of the loop equations!

In practice, you take a quick look at the diagram, and choose the two loops that look simplest …

in this case, I'd leave out the left-hand loop, because it has 4 items in it, while the other two loops have only 3.