Calculating Battery Internal Resistance: V=IR Method

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To calculate the internal resistance of a battery with an emf of 24V and a terminal voltage of 22V when connected to a 7.5-ohm resistor, the voltage drop across the internal resistance is 2V. The current through the circuit can be calculated using Ohm's Law, yielding a current of approximately 2.93A. By applying the formula for internal resistance (R = V/I), the internal resistance is determined to be 0.68 ohms. The confusion arose from incorrect application of the formulas and not properly accounting for the voltage drop and current. Understanding these calculations is crucial for accurate determination of battery characteristics.
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1. A battery is manufactured to have and emf of 24V, but the terminal voltage is only 22V when the battery is connected across a 7.5ohm resistor...what is the internal resistance of the battery?




3. Ok I have the answer already which is .68ohm...but I can't find a way to get to it. At first I tried V=IR or 24=I*7.5 and then plugged that answer into the same equation but with the voltage of 22. I also tried the opposite way. That answer didn't work.

I also tried subtracting the volts from each other to get .27R. Can someone please tell me what I am doing wrong?
 
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Answer these questions:
What's the voltage drop across the internal resistance?
What's the current through the circuit?
Combine these two answers to find the internal resistance.
 

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