Help with physics! (Interal resistance and EMF)

[Llama]

Hi gus,
I have an ISA to do tomorrow on internal resistance, but I almost get stuck on internal resistance, I can't get my head around it.

Let's say I have a battery with emf of 4.5v.

(emf = IR + Ir)

It's connected in series to a 12ohm resistor which reads 3v.

How do I figure out the current and the value of r?

 

[Dan]

I am not sure about what notation that is. Is x the cross product or just multiplication, either way doesn't really make sense to me.

But either way, current is easy. On a single closed circuit like you describe, Kirchoff's Current Law means that current through the resistor is the same current everywhere. So V=IR gives you the current through the entire circuit, 0.25 amps.

If r refers to internal resistance in the battery and the circuit, that is just 6 amps then. But that seems kinda high to me, and makes the whole question a bit too easy.

 

[Llama]

yh x being multiplication.
That isn't the exam question, just an example xD. Ok those are the answers I got aswell.

 

[Dan]

Then you should note that emf != IRxIr.

Also, denoting two resistances with capital and lower case letters in the same area as emf is kind of dicey because emfs are referred to as fields or matrices which are commonly denoted with a capital letter versus lowercase for a local value. And x in this case could easily be mistaken for the cross product of two matrices. R_1 and R_2 or R and R_i would make more sense unless the lower case r is the convention you are given in class.

 

[Llama]

You are thinking too much, my friend this is AS level stuff. No one will make that mistake because no one is supposed to know about it, heh heh.

Since I'm here, anyone whip up any similiar questions for me to try?


Edit: Should be +, not x, sorry. I r a muppet xD

 

[mindless_moder]

Dan is right , since 3 volts is dropped on the resistor the remaining (4.5-3) = 1.5 volts must be dropped on the internal resistance in the battery to satisfy Kirchoff's voltage law. The current through this resistance is the same as the current (3/12=0.25) through the 12 ohm since they're in series , so all you have to do is divide 1.5 by 0.25 which gives 6 volts.