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: However, this leads to incorrect answers: 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?