Desperately needing help on a simple Kirchoff problem

[Cetullah]

Hello people, this time I request your help for a fairly easy question, but a crucial one for me. To be honest I wasn't full awake when my teacher in university was talking on this topic( :( ), so I don't know how to solve it.

Homework Statement

Given on attachment. (Superior paint skills detected)

Homework Equations

Eh, not sure if I really need to say that, but the currents that moves in and moves out from a junction must be equal.

The Attempt at a Solution

I think I ve found the currents which batteries drive on the circuit. 50 V battery drives in 4.5 A, while 40V drives in 4.3 A.

 

[gneill]

Hello people, this time I request your help for a fairly easy question, but a crucial one for me. To be honest I wasn't full awake when my teacher in university was talking on this topic( :( ), so I don't know how to solve it.

Homework Statement

Given on attachment. (Superior paint skills detected)

Homework Equations

Eh, not sure if I really need to say that, but the currents that moves in and moves out from a junction must be equal.

The Attempt at a Solution

I think I ve found the currents which batteries drive on the circuit. 50 V battery drives in 4.5 A, while 40V drives in 4.3 A.

There are several possible approaches to solving this circuit employing Kichhoff's laws (KVL and/or KCL).

The current values you've found don't look right. Can you show your work?

 

[Cetullah]

Ah sorry, I have tried to solve the problem again, and found different values. Here is my path:

Currents on junction that is between the two 10Ω's:(1)
i₁+i₂=i₃

Currents on left loop: (2)

50-10i₁-20i₃+5i₁=0

50-5i₁-20i₃=0

10-i₁-4i₃=0

Carrying the equation (1) into 2:

10 - (i₂+i₃) - 4i₃=0

10-i₂-i₃-4i₃=0

10-i₂-5i₃=0

Currents on right loop:(3)

40+20i₃-10i₂=0

4+2i₃-i₂=0

Solving the equations:

10-i₂-5i₃=0

-4 + i₂ - 2i₃=0

6-7i₃=0

i₃=6/7=0.85

i₂=5.7

i₁=6.55

Hoping if these are correct :)

 

[azizlwl]

1.There are 3 unknown current flowing in the circuit so you need 3 equations. There are 3 loops, left, right and the outer.

2. Mark you resistor voltage drop sign, positive or negative at its terminal. The point of current entering is positive and leaving negative.

 

[gneill]

You have some sign issues in the loop equations (1) and (3). Your first equation, $$i_1 + i_2 = i_3$$ defines the current directions at the top center node, and you need to respect the those implied directions when you write the KVL loop equations.

Here's your diagram with the implied current directions indicated:

It is often helpful to mark in the implied potential rises/drops on the individual resistors before setting out to write the KVL equations