- #1

User11037

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## Homework Statement

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

## Homework 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

## 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:

However, this leads to incorrect answers:

By Kirchoff's 1st law, I

_{2}= I

_{0}+ I

_{1}

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 I

_{0}

V = IR, V = 20 x I

_{1}

So 20 x I

_{0}+ 20 x I

_{1}= 4

Using I

_{2}= I

_{0}+ I

_{1}from earlier,

20 x I

_{2}= 20 x I

_{0}+ 20 x I

_{1}

substituting this into 20 x I

_{0}+ 20 x I

_{1}= 4

gives 20 x I

_{2}= 4

I

_{2}= 4 / 20 = 0.2A

Applying Kirchhoff's 2nd law to the big loop (ie ignoring middle resistor):

EMF = 10 + 4 = 14V

∑PDs = 80 x I

_{2}+ 20 x I

_{0}

80 x I

_{2}+ 20 x I

_{0}= 14

80 x 0.2 + 20 x I

_{0}= 14

I

_{0}= -0.1A

I

_{2}= I

_{0}+ I

_{1}

I

_{1}= 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?