Solving Kirchhoff's Rules: Find Currents in a Circuit w/2 Batteries

[BOAS]

Hi,

i'm stuck on this problem and have been trying to identify where I might have made an error but have come up empty. I have assigned my loops and junctions and have three equation for three unknowns, but can't seem to solve them...

Homework Statement

Consider the circuit in the following diagram (attached):

where the two ideal dc batteries deliver a terminal voltage of V₁ = 2V and V₂ = 10V respectively. The magnitude of the resistances is R₁ = 2Ω; R₂Ω = 2; and R₃ = 3Ω. Calculate the magnitude and direction of the current across the resistor R₂.

Homework Equations

Kirchhoff's junction and loop rule.

The Attempt at a Solution

I₁ = I₂ + I₃ (JR)

v₁ - I₁R₁ - I₂R₂ = 0 (loop A)

-I₃R₃ + V₂ + I₂R₂ = 0 (loop B)

I can't see how to solve for any of these, which is making me think I've worked out the expressions wrong, but I can't find the mistake.

Thanks for any help you can give,

BOAS

 

[gneill]

Your equations look fine. Must be something to do with your mechanics of solving the equations. Guess you'll have to provide some details there.

 

[Tanya Sharma]

I₁ = I₂ + I₃ (JR)

v₁ - I₁R₁ - I₂R₂ = 0 (loop A)

-I₃R₃ + V₂ + I₂R₂ = 0 (loop B)

Your work looks fine.

You have three equations and three unknown so there should be no problem .From first equation find the value of i3 and substitute into 2nd and 3rd equations .You will be left with two equations and two unknowns.

 

[BOAS]

Your work looks fine.

You have three equations and three unknown so there should be no problem .From first equation find the value of i3 and substitute into 2nd and 3rd equations .You will be left with two equations and two unknowns.

I₃ = I₁-I₂

Subbing into the 3rd equation gives;

V₂ + I₂R₂ - (I₁-I₂)R₃ = 0

I don't see what you meant, when you said to sub I₃ into the second equation.

 

[Tanya Sharma]

v₁ - I₁R₁ - I₂R₂ = 0 (loop A)

V₂ + I₂R₂ - (I₁-I₂)R₃ = 0

Now you have two equations and two unknowns i1 and i2.The values of V1,V2,R1,R2.R3 are given in the problem statement. Just solve the two equations.

 

[BOAS]

Now you have two equations and two unknowns i1 and i2.The values of V1,V2,R1,R2.R3 are given in the problem statement. Just solve the two equations.

I've been making this far hard than it needs to be - I definitely need to go back and practice simultaneous equations again. I had completely forgotten to multiply the equations by a number to make elimination possible.

Multiplying V₁ - I₁R₁ - I₂R₂ = 0 by 3/2 makes the elimination work.

I get an answer for I₂ = -7/8 A which means the current goes the other way round.

Thank you for your help.