# Determining EMF and Internal Resistance

Basically I have been given this question:

A battery of unknown EMF and internal resistance is connected in series with an ammeter and a resistance box. The current was 2.0A when R= 4.0 Ohms and 1.5A when R= 6.0 Ohms. Calculate the EMF and internal resistance.

I feel you may have to arrange this somehow although I am probably wrong:

Internal resistance = v1-v2/I2-I1

I have had no attempt at a solution as I am utterly confused by this question.

x

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rl.bhat
Homework Helper
Hi joseppi, welcome to PF.
You have to write two equations for two resistances.
Use the equation
I = E/(R + r). Here r is the internal resistance.
Then solve for r.

Hi, sorry for me not having understood your instruction but how can I use the below equation for the answer if I have neither the: r or the E value?

I = E/(R + r)

x

E in this case is the emf, which you can work out with Ohm's Law.

rl.bhat
Homework Helper
You can write two equations for two resistances. With two equations you can find two unknowns.
I1 = E/(R1 + r)-------(1)
I2 = E/(R2 + r)-------(2)
Substitute the values given in the problem. Try to eliminate one unknown to find the other unknown.

2A = ?E/ (4.0 Ohms + ?r)

1.5A = ?E/ (6.0 Ohms + ?r)

I'll be honest I am quite bad with Maths even though I take AS level physics. I have no clue how to eliminate the r or E unknown or even really how to move it around ;/ You couldn't explain how and why you do this? It would be a great help, thank you.
x

rl.bhat
Homework Helper
From the first equation
E = 2A(4.0 Ohm + r)----(1)
Similarly from the second equation write E = ........---(2)
Equate eq 1 and 2, and solve for r.