1. The problem statement, all variables and given/known data See above diagram for full details of the circuit Variables used: Assumption: direction of current is clockwise and the loops are positive in clockwise as well. Current through 1000 ohm=i1 Current through 4700 ohm-i2 Current through 2200 ohm=i3 Current through 1200 ohm=i4 Please note there are 2 junctions present across 2200ohm resistor. Thanks! Problem: we have to find the total current (I) and the branch currents (i1, i2...i4) using Kirchoffs laws. 2. Relevant equations Using kicrhoffs current law: i1=i3+i2 i3+i2=i4 Therefore i1=i4 Using kicrhoffs voltage law: Loop 1: 12=1000i1+2200i3+1200i1 (since i1=i4) Loop 2: 0=4700i2+2200i3 3. The attempt at a solution Loop 1: 12=2200i1+2200i3 (simplification) But i1=i2+i3 => 12=2200i2+4400i3 Solving loop 1 and loop 2 eqn's simultaneously gives: i2=-1/600A (isn't the current supposed to go towards the negative terminal?) Substitution into loop 1 eq'n gives: i3=47/13200A Now the problems: (1) if i1=i3+i2 then should |i2| be used or i2 to substitute in for the i2 in the equation mentioned? (2) also having found i2, i1, and i3, then is the summation (with or without modulus of i2?) of these branch currents equal to source current? (3) assuming the" e.m.f source current ≠ branch currents summation" (as asked in question (2), correct my thinking please); the question is should I simplify the circuit (parallel and series resistors to an equivalent resistor and then using E=IV) and calculate source current using ohms law? I ask this because the question asks for usage of kirchoffs laws (underlined in the problem) to find branch currents and the source current.