How Do You Calculate a Battery's Voltage with Different Resistors?

[fran1942]

Hello, the question I am trying to solve is:

A battery has a terminal voltage of 8V when it is connected to a 8 Ohm resistor, and a terminal voltage of 6V when it is connected to a 3 Ohm resistor. Calculate the values of the battery circuit components.

I went about it like this:
(using 'VS' to represent battery EMF and 'r' to represent battery internal resistance)
I implemented the formula for battery voltage, and created two formulas for each situation:

A: Vbatt (8) = VS - (1Amp * r)
B: Vbatt (6) = VS - (2Amps * r)

simplified to:
8 = VS - 1r
6 = VS - 2r

Evaluating these two linear equations gave me:
'r' (internal resistance) = 2 Ohms.

I was now asked to: "calculate the battery's voltage while it is charged with a 1A current."

But I now realized I would end up with two different voltage value answers for this question, because I have two current values and therefore two VS values.

I think I have gone wrong somewhere. I think there should only be 1 voltage value answer ? - Can anyone see what I am missing ?

Thanks kindly for any help

 

[gneill]

You had two equations in two unknowns, r and VS. You only stated what value you found for r. What value do you get for VS from those two equations?

 

[fran1942]

thanks for helping.

I got:
A: VS = 8 + 1r (VS=10)
b: VS = 6 + 2r (VS=10)

therefore the answer to the second question (calculate the batteries voltage while it is charged with a 1 A current) is:
Vbatt = VS - Ibatt*r
Vbatt = 10 - 1*2
Vbatt = 10-2
Vbatt = 8V

I think I understand it all now.

 

[gneill]

Beware of the polarity of the voltage being developed on the internal resistance. When the battery is being charged, current is flowing into the battery's positive terminal, not out of it as when it's connected to a load.

 

[rwisz]

providedHi there,

First of all, great job on using the formula for battery voltage and creating two equations to solve for the internal resistance (r). You are correct in saying that there should only be one voltage value answer for this question.

To clarify, the two equations you created represent two different situations - one where the battery is connected to an 8 Ohm resistor and another where it is connected to a 3 Ohm resistor. In both situations, the current (Amps) is different, which is why you have two different equations. However, the internal resistance (r) remains the same in both situations.

So, to solve for the battery's voltage when it is charged with a 1A current, we can use either equation. Let's use the first equation (A) since it has the same current value as the question given.

8 = VS - 1r
8 = VS - 1(2)
VS = 10V

Therefore, the battery's voltage while charged with a 1A current is 10V.

I hope this helps clarify any confusion you had. Keep up the good work in your scientific calculations!