# Multiple EMFs in a circuit

## Homework Statement

So this is not really a 'solve this problem' question, but, rather, I am trying to understand how they can call ABCDEFA a 'closed loop' even though there is another connection (BE) inside it, and why the equations work.

Keeping in mind that I am still in high school physics, and this is definitely outside the scope of this course (hence I cannot rely on my teachers!), I will attempt to reason it out, using Kirchoff's laws.

## The Attempt at a Solution

Why would ABCDEFA be a closed loop? I am assuming that it is because no current can enter or exit the loop?
Could someone explain the actual definition of a closed loop here? If the conductor BE were not present, I would have no problem stating that ABCDEFA were a closed loop. But BE just messes me up!

They use Kirchoff's Second Law to get the first equation (yellow). But up to now I've only encountered single EMF circuits. Could someone direct me to get some intuition about why E2 does not affect this equation?

I can't really reason it out much more... except perhaps the fact that, if we ignore E2 and E3, (hence making it into a single EMF circuit), BE and CD are in parallel, and the voltage drops are the same...

Some help would be much appreciated!

Stephen

rude man
Homework Helper
Gold Member
There is an oval racetrack but there is also a straight short-cut in the middle of said oval track joining midpoints of opposite sides of the oval track.

I can run a closed loop around the large oval track. But I can also run a closed loop around one half of the oval track plus the shortcut. Wouldn't you say both ways are closed loops? You wind up where you started, that is the critrerion.

Now you're an electron & you can run all the way around either the full oval or half the oval plus the short-cut.

NascentOxygen
Staff Emeritus
A closed loop is just a path that ends up where you started from, and is continuous with no gaps. Currents in the various parts can be different (which means other branches can lead in or out from some of the nodes). The main point is that the sum around the loop of all the individual voltage differences is zero
i.e., the voltage rises = the voltage drops, in total

CWatters
Homework Helper
Gold Member
Personally I'm not a fan of the way they have written their equation. I much prefer to write it so that it really does sum to zero....

I1R2 + I3R4 + + I3r3 + (+E3) + I3R5 + I4R6 + I1r1 + (-E1) + I1R1 = 0

You can then rearrange it but I find that way you are much less likely to make a mistake.

I'm also not happy with their statement that "E1 and E3 send currents in the clockwise direction". They might do but it's not necessarily true. I think it's better to write..

"I1 and I3 are defined such that clockwise is positive"
and
"I2 is defined such that downwards is positive"

For example if E2 was very large I2 and I1 might be negative (eg flow anticlockwise).