Should same values of currents be used in Kirchoff's laws?

[Sol_Engineered]

Homework Statement

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.

Homework 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

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 kirchhoffs laws (underlined in the problem) to find branch currents and the source current.

 

[mfb]

There is no need to use Kirchhoff's laws here, but if the problem statement wants you to use them... well.

Loop 2: 0=4700i2+2200i3

If you go around the loop, one current will get a negative sign because . Fix that and everything will work out.

The source current is the current in loop 1, there is no need to add anything.

 

[Sol_Engineered]

. I checked out that total current (using alternative method) is same as that in I1. I can't seem to make myself clear that why would total current be same as in I1?

 

[mfb]

The source and R1 are in series. What else would you expect?

 

[Sol_Engineered]

The source and R1 are in series. What else would you expect?

Ah so battery can be in series like a resistor!

Sorry first year of mechanical engineering and I feel so dumbThanks mate

 

[mfb]

Ah so battery can be in series like a resistor!

All components can be in series. There is nothing preventing you from putting them in the right spot in a circuit, neither on paper nor wíth actual wires.