Finding potential at a specific point in the circuit Help

[koab1mjr]

Finding potential at a specific point in the circuit... Help!

Homework Statement

....... ground
.......|
----R2-------------------
|......|...|
|......|...|
|......|...|
R1......R3...R4
|......|...|
|......---------
|......|
Emf1.....Emf2
|......|
|......|
V2-----R5-------V1

dots are for spacing that is all


The resistances are all 2 ohms and emf1 = 5V and emf2 =12 V
what are the potentials at points V1 and V2

Homework Equations

currents are noted by what resistor they flow through
I₁ = I₂ = I₅

I used the following equations
junction rule
I₁ = I₄ + I₃
loop rule
Emf₁ - I₁R₁-I₁R₂-I₃R₃-emf₂-₁R₅ = 0

Emf₁ - I₁R₁-I₁R₂-I₄R₄-emf₂-₁R₅ = 0

The Attempt at a Solution

Using the above I found I₁ = 1amp, I₃ = 0.5 amp and I₄ = 0.5 amp

Now where i am stuck is when trying to find the potential at a point. This is the first time i seen such a problem related to a circuit. Before I seen difference between two points or something like that or voltage at a resistor or something but V1 and V2 are on the wires. I tried taking two separate pathes between V1 and V2 but that did not pan out.

I just looking for some hints on how to approach

thanks in advance

 

[LowlyPion]

I think you are making it more complicated than it needs to be.

Since R3 || R4 that means you can replace it with the equivalent R for the 2.

I can't see which direction your Voltage sources are pointing, but you seem to indicate that they are opposing each other through R5, so that suggests that difference of the Voltages 7V is the effective voltage delivered through all the resistors. So I = 7v/Req of all the resistors.

Armed with the current I, then simply figure your V1 and V2 from the relative step up or step down from the ground reference.

 

[koab1mjr]

[Solved]

Thank you so much Lowly, now that you mention it. The solution is easy. -11V for V1 and - 9V for V2.

I probably did make it over complicated with loops, but is there any circumstance where one cannot reduce all the resitances to a single Req.

 

[LowlyPion]

[Solved]

Thank you so much Lowly, now that you mention it. The solution is easy. -11V for V1 and - 9V for V2.

I probably did make it over complicated with loops, but is there any circumstance where one cannot reduce all the resitances to a single Req.

It depends really on what you are trying to do. If all the resistances do resolve into an equivalent then of course. But if you have a mesh of nodes with multiple active sources, then maybe you would want to just simplify the ones that make your life easier.

Of course a computer programmed generalized solver would just analyze every node and loop and take the mess of equations and solve them faster than you can say Bob's your uncle. Basically I guess between the two extremes let common sense be your guide.