Circuit source current question

[orangeincup]

Homework Statement

Find is of the circuit below

Homework Equations

i=V/R
v1+v2+..=0
is=vs/Req

The Attempt at a Solution

Resistance of circuit as seen by source = 7kΩ
6V(source)/7kΩ(Req)=.857i

My question is, how come i3 is also 0.857i? Shouldn't it be different since it just went through two resistors? Can someone explain to me why the currents are the same? Is it because the resistances are in series?

 

[gneill]

i_s alone leaves the voltage source, while i₃ alone re-enters the voltage source. You can't have one different than the other through the same component...

 

[orangeincup]

If it had another current source or voltage source below one of the resistors, would this still be true?

 

[gneill]

If it had another current source or voltage source below one of the resistors, would this still be true?

There is no way that the current entering a component can be different from the current leaving it. Otherwise charge would be building up on the component or be created or destroyed. Can't happen! Components in series all carry exactly the same current.

If you change the circuit so that i3 is no longer solely feeding the one voltage source but has some other path available (so it feeds into a node shared with the voltage source and something else, perhaps leading to another voltage source), then you no longer have the same setup and that other "something" may contribute to the total current making its way to the voltage source.