Internal resistance of a battery

AI Thread Summary
To determine the internal resistance of a battery given two different resistances and currents, the equations E = I(R + r) can be utilized. With a 10.5-ohm resistance and a 2-amp current, and a 48-ohm resistance with a 0.5-amp current, two equations can be set up to solve for both the electromotive force (EMF) and internal resistance (r). By assuming the EMF remains constant, these two equations can be solved simultaneously to find the values of EMF and internal resistance. This approach allows for the calculation of internal resistance despite having two unknowns. Understanding this method is crucial for solving internal resistance problems effectively.
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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.
 
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