# Internal resistance of a battery

Ok guys I need help! Its been a while since I last opened a physics workbook and now I'm back to studying to try and further my career and I've come across an internal resistance question that I can't get my head around!

A resistance of 10.5 ohms is connected across the terminals of a battery and a current of 2 amps flows. When this resistance is replaced by another resistance of 48 ohms a current of 0.5 amps flows. The internal resistance of the battery therefore equals?

The only equation I've come up with is E = I(R+r)

So to work out the internal resistance of the battery I need to work out the emf first to use the above equation but how do I do that? I thought of using similar equations but that will only work if there is one unknown in the equation not two right?

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You can set up two such equations with the two values of resistance and current. Assuming the battery EMF doesn't change, you can then solve the 2 equations for EMF and internal resistance.