Kirchhoff's law problem with two batteries

[patric44]

Homework Statement

find the value of E1 that would make the reading of the ammeter = 0

Relevant Equations

I3 = I1+I2
E1 = 3I1 + 4I3
12 = 2I2 + 4I3

the question is find the value of E1 that would make the ammeter reading = 0 ?
i tried KCL , and KVL and got the following equations : ( I₁ belongs to 3 ohm , I₂ belongs to 2 ohm , I₃ belongs to 4 ohm ):
I₃ = I₁+I₂
E1 = 3I₁ + 4I₃
12 = 2I₂ + 4I₃

but now i have 3 equations in 4 variables ?!
i think its simpler than that but i am missing the idea here , any help on this ?
i saw the answer it equals 8 v , but i can't get any further with my equations .

 

[kuruman]

Don't think of this as a system of $n$ equations and $n$ unknowns that you have to solve. You want $I_1$ to be zero, so get an equation involving $E_1$, $E_2$ and $I_1$ by eliminating the other two currents and see for what value of $E_1$ the value of $I_1$ is zero. Alternatively, set $I_1=0$ in your equations and solve a system of 3 equations and 3 unknowns. You can do that in your head.

 

[sojsail]

Another approach: You know that the ammeter reading is to be zero. So assume that is the case and simplify your equations accordingly.

 

[DaveE]

but now i have 3 equations in 4 variables

But you know the value of one of those variables from the desired solution (ammeter current = 0).

 

[patric44]

Don't think of this as a system of $n$ equations and $n$ unknowns that you have to solve. You want $I_1$ to be zero, so get an equation involving $E_1$, $E_2$ and $I_1$ by eliminating the other two currents and see for what value of $E_1$ the value of $I_1$ is zero. Alternatively, set $I_1=0$ in your equations and solve a system of 3 equations and 3 unknowns. You can do that in your head.

thank you so much once you said I1 = 0 it hit me , i calculated it and it came out 8 v .