Does the voltage across a battery include its internal resistance?

In summary, the voltage across a battery does include its internal resistance. The total voltage, known as the electromotive force (EMF), is the potential difference when no current flows. However, when a load is connected, the internal resistance causes a voltage drop, resulting in a lower terminal voltage. Therefore, both the EMF and internal resistance are crucial in determining the actual voltage available for external use.
  • #1
laser
104
17
Homework Statement
See description
Relevant Equations
V=iR
Screenshot_4.png


I am uncertain if this represents situation (a) or situation (b).

Screenshot_6.png


i.e. is 2 = E-iR or is 2 = E? Or is the question ambiguous?

Thanks!
 
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  • #2
laser said:
Homework Statement: See description
Relevant Equations: V=iR

View attachment 344072

I am uncertain if this represents situation (a) or situation (b).

View attachment 344073

i.e. is 2 = E-iR or is 2 = E? Or is the question ambiguous?

Thanks!
Is the r in your diagrams a representation of the internal resistance? If so, it is (b).
The actual voltage on the terminals depends on the current, so it would not make sense to call it a 2V battery if it meant (a).
 
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  • #3
haruspex said:
Is the r in your diagrams a representation of the internal resistance?
Yes
 
  • #4
Just to add on to that: Battery voltage (or any voltage you measure really) is measured with a voltmeter connected to the terminals. The voltmeter has a large resistance as to not interfere too much with the measurement - an ideal voltmeter would have infinite resistance implying zero current through it.

Amperemeters are the opposite, they are connected in series in the circuit which you measure and need as low resistance as possible not to interfere with the circuit. An ideal amperemeter would have zero resistance.

Edit: Fixed typo.
 
Last edited:
  • #5
laser said:
Homework Statement: See description
Relevant Equations: V=iR

is 2 = E-iR or is 2 = E? Or is the question ambiguous?
How would you envisage measuring the value ξ in diagram b? You'd have to put the probes 'somewhere' in amongst the electrolyte and electrodes. emf is a value of potential difference when no current.is being taken. Internal resistance is just a mental construct which gives a value to the amount of energy dissipated inside the battery for each unit of charge that passes through. We don't know where the loss occurs and nor do we find that the value of r is the same for all currents. r is a handy value to tell us things like how 'good' a battery is and what sort of load it will support.
 
  • #6
Orodruin said:
Amperemeters are the opposite, they are connected in parallel in the circuit
We measure current in series, voltage in parallel.
 
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  • #7
DaveE said:
We measure current in series, voltage in parallel.
Yeah, I think that was just a typo in his reply, based on his "opposite" comment (which is correct). I've sent Oro a PM to clarify. :smile:
 
  • #8
Yes. That’s a typo clearly. Fixing.
 
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  • #9
The "ideal" battery we usually choose to use for analysis is the Thevenin equivalent of the "real" battery which is in fact more complicated internally..
 

FAQ: Does the voltage across a battery include its internal resistance?

1. What is internal resistance in a battery?

Internal resistance refers to the opposition to the flow of electric current within the battery itself. It is caused by factors such as the chemical properties of the electrolyte, the physical structure of the electrodes, and the temperature of the battery. Internal resistance can lead to energy loss in the form of heat and affects the overall performance of the battery.

2. Does the voltage across a battery change when current flows?

Yes, the voltage across a battery can change when current flows due to internal resistance. The actual voltage measured at the terminals of a battery under load (when current is drawn) is lower than its open-circuit voltage (when no current is flowing). This drop in voltage is a result of the internal resistance of the battery, which causes a voltage drop proportional to the current flowing through it.

3. How is the voltage across a battery calculated?

The voltage across a battery can be calculated using the formula: V = E - I * r, where V is the terminal voltage, E is the electromotive force (EMF) or open-circuit voltage of the battery, I is the current flowing through the circuit, and r is the internal resistance of the battery. This equation shows that the terminal voltage decreases as the current increases due to the voltage drop across the internal resistance.

4. Why is internal resistance important in battery applications?

Internal resistance is important because it affects the efficiency, performance, and lifespan of a battery. High internal resistance can lead to significant energy losses, reduced capacity, and increased heat generation during operation. In applications where high current is required, such as in electric vehicles, minimizing internal resistance is crucial for achieving optimal performance and efficiency.

5. Can internal resistance be measured?

Yes, internal resistance can be measured using various methods. One common approach is to apply a known load to the battery and measure the voltage drop across the terminals while the load is active. By using the formula for voltage drop (V = I * r), the internal resistance can be calculated. Additionally, specialized equipment like an impedance analyzer can provide more precise measurements of internal resistance across different frequencies.

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