Voltage Drop in Weak Batteries: Exploring the Equations

In summary: The potential difference between the anode and cathode of a battery can be mathematically explainable.
  • #1
Whakataku
12
0
Relevant equations:

V = I*R
ε = I*(R+r)
Then,
V = {ε/(R+r)}*r

V = potential difference, ε = electromotive force, R = resistance of external load resistor,
r = internal resistance of the battery.

So say the external load resistor's resistance is a constant for two batteries of the same make, difference being that one is good and the other is weak. Then since by intuition the internal resistance will be different, the good battery at room temperature having less r than the weak battery. The ε is constant.

Then is it correct to say that the voltage or potential difference will be smaller, or there will be voltage drop for the weak battery compared to the good battery?
 
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  • #2
Whakataku said:
Relevant equations:

V = I*R
ε = I*(R+r)
Then,
V = {ε/(R+r)}*r

V = potential difference, ε = electromotive force, R = resistance of external load resistor,
r = internal resistance of the battery.

So say the external load resistor's resistance is a constant for two batteries of the same make, difference being that one is good and the other is weak. Then since by intuition the internal resistance will be different, the good battery at room temperature having less r than the weak battery. The ε is constant.

Then is it correct to say that the voltage or potential difference will be smaller, or there will be voltage drop for the weak battery compared to the good battery?

It depends on the type of battery, but often you will not see much difference in the open circuit voltage for much of the discharge cycle. Most of the droop comes near the end of the discharge cycle.

You can look at the battery's datasheet to see what its discharge curves look like. This is a curve for a deep-discharge battery:

http://hamwaves.com/qrp/portable/dm12-7.2_discharge.gif
dm12-7.2_discharge.gif
 
  • #3


What do you mean by a "weak" battery? Do you mean a battery that is nearly discharged or do you mean a rechargable battery that has nearly lost its ability to store a charge? My knowledge and experience pertains mostly to lead-acid batteries but I can tell you the following about them...

Open circuit voltage of a fully charged lead-acid cell is about 2.1 volts, it will deplete about 75% of its capacity before dropping to 2.0 volts. The same applies to a cell that is nearly worn out, though the capacity will be lower, the internal resistance will be higher, and the recovery time will be longer. (recovery time is how long it takes the open circuit voltage to come back up after a load is removed)
 
  • #4


Sorry I didn't specify a battery. Let's just say a D cell alkaline battery with 1.5V. And by weak, I mean, nearly discharged, or nearly depleted in chemical charge due to the extensive oxidation reaction at the anion.

You see what I'm getting confused is that I ask someone about it and they say one thing, and ask another person they say the totally different thing. I just want to know if the voltage is dependent on the internal resistance, or totally independent like the electromotive force which is due to the chemical reaction within the cell. The equations I mentioned seems to indicate the former where the potential difference is dependent on the internal resistance.

The chart was helpful Berkeman, but are there any universal mathematical statement that relates the internal resistance to the voltage of an electromotive cell?

Regarding mrspeedybob "Open circuit voltage of a fully charged lead-acid cell is about 2.1 volts, it will deplete about 75% of its capacity before dropping to 2.0 volts. "
Was what you stated a phenomenon, or can it be mathematically explainable?
I crave mathematical proof regarding the potential difference between the anode and cathode of a battery.
 
Last edited:
  • #5


Yes, it is correct to say that the weak battery will experience a smaller voltage or potential difference compared to the good battery due to the higher internal resistance. This is because, as per the equation V = {ε/(R+r)}*r, the voltage drop (V) is inversely proportional to the internal resistance (r). Therefore, a higher internal resistance will result in a smaller potential difference. This is why weak batteries are not able to provide the same amount of power as good batteries, as they experience a greater voltage drop. This also explains why weak batteries may not be able to power devices that require a higher voltage.
 

1. What is voltage drop in weak batteries?

Voltage drop in weak batteries refers to the decrease in the amount of electrical potential that a battery can provide as it becomes drained or depleted.

2. How does voltage drop occur in weak batteries?

Voltage drop occurs in weak batteries due to a decrease in the amount of chemical energy available to produce electrical potential. This can be caused by factors such as age, usage, and environmental conditions.

3. What equations are used to calculate voltage drop in weak batteries?

The two main equations used to calculate voltage drop in weak batteries are Ohm's Law (V=IR) and the power equation (P=IV). These equations take into account the resistance and current of the battery to determine the voltage drop.

4. How can voltage drop in weak batteries affect electronic devices?

Voltage drop in weak batteries can cause electronic devices to malfunction or not work at all. This is because the decrease in electrical potential may not be enough to power the device or maintain its proper functioning.

5. Can voltage drop be prevented in weak batteries?

Voltage drop in weak batteries cannot be prevented, but it can be managed. Regularly replacing old or weak batteries with new ones can help prevent voltage drop and ensure proper functioning of electronic devices.

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