# Directions of currents in Kirchhoff's 2nd law problems

1. Feb 20, 2014

### User11037

1. The problem statement, all variables and given/known data

Apply Kirchhoff's laws to find the current at point X in the circuit shown. What is the direction of the current?

2. Relevant equations

V = IR
Kirchhoff's 1st law: ∑Currents entering junction = ∑Currents leaving junctions
Kirchhoff's 2nd law: ∑EMFs in a loop = ∑PDs in a loop

3. The attempt at a solution

This problem is simple enough but my issue is how to tell initially which directions the currents are going in. My initial approach was as follows:

By Kirchoff's 1st law, I2 = I0 + I1
By Kirchoff's 2nd law, the sum of the emfs in the top loop must equal the sum of the pds:
EMF = 4V
PDS:
V = IR, V = 20 x I0
V = IR, V = 20 x I1
So 20 x I0 + 20 x I1 = 4
Using I2 = I0 + I1 from earlier,
20 x I2 = 20 x I0 + 20 x I1
substituting this into 20 x I0 + 20 x I1 = 4
gives 20 x I2 = 4
I2 = 4 / 20 = 0.2A

Applying Kirchhoff's 2nd law to the big loop (ie ignoring middle resistor):
EMF = 10 + 4 = 14V
∑PDs = 80 x I2 + 20 x I0
80 x I2 + 20 x I0 = 14
80 x 0.2 + 20 x I0 = 14
I0 = -0.1A

I2 = I0 + I1
I1 = 0.2 -- 0.1 = 0.3 A which is not the correct answer.

Why should labelling the currents in this way not give the correct answer?

2. Feb 20, 2014

### SteamKing

Staff Emeritus
In these problems, if the assumed direction of the current is incorrect, the value obtained should just be the negative of the actual current magnitude. I haven't checked the set up of your equations, but there may be other problems there.

3. Feb 21, 2014

### Staff: Mentor

This equation is not correct. You have a sign wrong.

Once you have assigned directions to currents, you must pay close attention to polarities of associated potentials.