Calculating Battery Internal Resistance: V=IR Method

[accol]

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?

 

[Doc Al]

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.

 

[thomate1]

I would first like to commend you for attempting to solve this problem and seeking help when you encountered difficulties. It shows a strong critical thinking mindset and a willingness to learn.

Now, let's go through the steps to solve this problem using the V=IR method.

First, we need to understand the equation V=IR. This equation means that the voltage (V) across a resistor is equal to the current (I) flowing through the resistor multiplied by the resistance (R) of the resistor.

In this problem, we are given the emf (electromotive force) of the battery, which is the maximum potential difference it can provide. This value is 24V. However, when the battery is connected to a 7.5ohm resistor, the terminal voltage is only 22V. This means that there is a voltage drop of 2V across the resistor.

Using the V=IR equation, we can set up the following equation:

22V = I * 7.5ohm

Now, we need to solve for the current (I) flowing through the resistor. To do this, we divide both sides of the equation by 7.5ohm. This gives us:

I = 22V / 7.5ohm

Simplifying this, we get I = 2.93A. This means that there is a current of 2.93A flowing through the resistor.

Now, we can use this current value and the given voltage drop of 2V to calculate the internal resistance of the battery. We can rearrange the V=IR equation to solve for R, which gives us:

R = V / I

Substituting the values, we get R = 2V / 2.93A. Simplifying this, we get R = 0.68ohm. This is the internal resistance of the battery.

In summary, to calculate the internal resistance of the battery using the V=IR method, we need to first identify the voltage drop across the resistor, calculate the current flowing through the resistor, and then use these values to solve for the internal resistance. I hope this explanation helps you understand the problem and the steps to solve it. Keep up the good work!