Internal Resistance of a battery

In summary, the internal resistance of the battery affects the terminal voltage when a load is placed across the terminals. The terminal voltage is 11.0 volts when a 10 ohm load is used, but when a 100 ohm load is used, the terminal voltage is 11.9 volts.
  • #1
hey123a
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0

Homework Statement


When a 10 ohm load is placed across the terminals of a battery, the terminal voltage is 11.0V. When a 100 ohm load is used instead, the terminal voltage is 11.9V. What is the internal resistance of the battery?


Homework Equations



V=IR

The Attempt at a Solution



I do not know how to approach this question but I do know that I have to use V = IR. I also know that the terminal voltage occurs after the voltage drop from the internal resistance. Is this right? A hint on how to approach this question would be nice! Thank you
 
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  • #2
Draw the circuit you are dealing with, representing the battery itself as an ideal voltage source in series with a resistor, the resistor value at this stage being unknown, so call it Ri.
 
  • #3
NascentOxygen said:
Draw the circuit you are dealing with, representing the battery itself as an ideal voltage source in series with a resistor, the resistor value at this stage being unknown, so call it Ri.

I did do that. I feel like this question is impossible?
So, terminal voltage = IR

when using 10ohm resistor
terminal voltage = 11 = I(10)

when using 100ohm resistor
terminal voltage = 11.9 = I(100)

current should be the same in both cases, but when solving for current it isn't the same?
 
  • #4
hey123a said:
I did do that. I feel like this question is impossible?
So, terminal voltage = IR

when using 10ohm resistor
terminal voltage = 11 = I(10)

when using 100ohm resistor
terminal voltage = 11.9 = I(100)

current should be the same in both cases, but when solving for current it isn't the same?

Why would you think the current would be the same in both cases?

When Nascent said draw the circuit, what he meant was DRAW THE CIRCUIT. And put it here where we can see it. And show your work relative to the drawing.
 
  • #5
also, the answer to this question is 0.917
 
  • #6
phinds said:
Why would you think the current would be the same in both cases?

When Nascent said draw the circuit, what he meant was DRAW THE CIRCUIT. And put it here where we can see it. And show your work relative to the drawing.

If the same battery is used, shouldn't the current in both cases be the same?
Also here is a drawing of the circuit

Untitled.png
 
  • #7
after finding the currents for both cases, use the relationship you listed, V=IR. The internal resistance should be equal to [itex]\frac{ΔV}{ΔI}[/itex] in this case. which will get you the answer you had.
 
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  • #8
hey123a said:
If the same battery is used, shouldn't the current in both cases be the same?
Also here is a drawing of the circuit

View attachment 67052

I continue to be dumbfounded at how you can imagine that would be the case. Do you believe that a battery feeding a million ohm resistor draws as much current as the same battery feeding a 1 ohm resistor?
 
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  • #9
hey123a said:
If the same battery is used, shouldn't the current in both cases be the same?
If it is the same battery, then its model will be the same: same ideal voltage, same internal resistance.

Also here is a drawing of the circuit

View attachment 67052
Sorry, my mistake. I should have said, draw the circuits, because as you'll appreciate there are two circuits to deal with here. The first "when a 10 Ω load ..." and another "when a 100 Ω load ...". Two different circuits.

So draw those two circuits, marking on each all the information you know.
 
  • #10
hey123a said:
also, the answer to this question is 0.917
It must have units.
 
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  • #11
asdf12312 said:
after finding the currents for both cases, use the relationship you listed, V=IR. The internal resistance should be equal to [itex]\frac{ΔV}{ΔI}[/itex] in this case. which will get you the answer you had.

Okay i got the answer, thank you. the internal resistance is 0.917 ohms,
but can you please derive how you got [itex]\frac{ΔV}{ΔI}[/itex] ?

thank you
 
  • #12
If anyone still wants to know how here:
V = terminal voltage, E = EMF of battery, I = current from tests (will be different depending of resistances), r = internal resistance.
V = E - Ir... This eqn states that the voltage exiting and entering the terminals is equal to the total emf the battery would have without the internal resistance, minus the little bit of voltage drop in the battery due to internal resistance.
Now subtract these equations derived from both scenarios (E is a constant so it cancels out)
(V1 = E - I1r) - (V2 = E - I21r)
Now:
V1 - V2 = -I1r + I2r
Factor out the r:
V1 - V2 = (-I1 + I2)r
divide:
(V1 - V2)/(-I1 + I2) = r
or:
∆V/∆I = r
To Find I by the way, use V = IR, make it I = V/R, use the values given in the question, and plug em in.
 

1. What is internal resistance of a battery?

The internal resistance of a battery is the opposition to the flow of electric current within the battery itself. It is caused by the resistance of the materials used in the battery and the chemical reactions that take place inside it.

2. How is internal resistance measured?

Internal resistance is typically measured by connecting a known external resistance to the battery and measuring the voltage drop across it. The internal resistance can then be calculated using Ohm's Law (R=V/I), where R is the internal resistance, V is the voltage drop, and I is the current flowing through the external resistance.

3. What factors affect the internal resistance of a battery?

The internal resistance of a battery can be affected by several factors, including the type of battery (e.g. alkaline, lithium-ion, etc.), the size and design of the battery, the age of the battery, and the temperature. Higher temperatures can increase the internal resistance of a battery, while lower temperatures can decrease it.

4. How does internal resistance affect battery performance?

Internal resistance can have a significant impact on the performance of a battery. The higher the internal resistance, the more energy is lost as heat and the less energy is available for use. This can result in a decrease in voltage and a shorter battery life. It can also cause the battery to heat up and potentially damage the device it is powering.

5. Can internal resistance be reduced?

While the internal resistance of a battery cannot be completely eliminated, it can be reduced by choosing a battery with a lower internal resistance, using the correct type and size of battery for the device, and keeping the battery at a moderate temperature. Additionally, regularly charging and properly maintaining the battery can help to reduce its internal resistance over time.

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