WHY does source voltage drop with the increase in current?

Thread Starter

Beetle_X

Joined Nov 2, 2012
52
There are a lot of guides that state that this is caused by internal resistance of the source but not why. Here's the formula V = emf − Ir.Does increasing current increase resistance so the resistance is not a constant?

Thank you for your expertise!
 
Last edited:

Audioguru again

Joined Oct 21, 2019
1,908
Increasing the current causes a higher voltage drop across the internal resistance which reduces the source voltage.
Some resistances increase their resistance when the current is increased caused by heating.
 

Papabravo

Joined Feb 24, 2006
14,393
No. The source resistance is an inherent property of the voltage source. It is nearly constant, and as the current increases, that constant resistance drops more of the source voltage. Look at the typical discharge curves for different types of batteries and notice what happens as the battery reaches it's end of life.
 

Thread Starter

Beetle_X

Joined Nov 2, 2012
52
Thanks for both of the replies! I can't find a clear reason for this with batteries. What about a generator?
 

Papabravo

Joined Feb 24, 2006
14,393
Thanks for both of the replies! I can't find a clear reason for this with batteries. What about a generator?
The reason is right in front of you but you refuse to acknowledge it. There is no such thing as an ideal voltage source. The source resistance is the deviation of a real source from ideality. In this regard, generators are no different than batteries.
 

WBahn

Joined Mar 31, 2012
26,143
Thanks for both of the replies! I can't find a clear reason for this with batteries. What about a generator?
WIth batteries, the underlying reasons is in the details of the chemical reactions. With no load, the terminal voltage builds up to its open circuit value when it is sufficiently high enough to suppress further chemical reactions in the cell. But without the chemical reactions, no current can flow. So for there to be any current, the voltage has to drop so that the chemical reactions can start up again. With a small voltage drop, only a small amount of chemical reaction can take place (most of it is still suppressed). So to get more current, the voltage has to be even lower. Hence, more current, lower voltage. This happens naturally. Let's say that you have a battery that has an open circuit voltage of 100 V and that it has an internal resistance of 1 Ω. That 100 V is the result of a charge separation resulting from the chemical reactions and at 100 V those reactions stop and the charge separation on the terminals maintains that 100 V. Now lets say you put a 9 Ω load across the terminals and let it sit there and settle down. You will have 10 A flowing and a terminal voltage of 90 V. What happens in the load resistance goes up a bit? The current will drop but the chemical reactions are still producing the 10 A of current it can produce with a terminal voltage of 90 V, so the excess current will build up on the terminals, thus raising the terminal voltage to a bit more than 90 V. If the load resistance were to go down, the load would draw more than the 10 A being produced by the cell with a terminal voltage of 90 V and the terminal voltage will drop, but this will result in more chemical reaction occurring and the output increasing as a result. The amount of charge associated with the charge separation the produces the terminal voltage is truly minuscule, so these changes occur almost instantly.

With generators it generally with the physical resistance of the components in the generator. You can design active power supply circuits that monitor the output voltage and increase or decrease the driver signal in order to keep the voltage at the terminal constant regardless of current draw. If the supply uses a symbol proportional controller to do this, then the effective output impedance will be small, but not zero because an error signal is needed in order to produce the drive signal. But if the controller has an integral term, the error will be driven to zero and the supply will look like it has zero output impedance, at least in steady state.
 

MisterBill2

Joined Jan 23, 2018
6,998
Thanks for both of the replies! I can't find a clear reason for this with batteries. What about a generator?
Effective source resistance is found in ALL voltage sources. The amount varies, but it is always present. In some situations it may not matter, but source resistance is intrinsic. A well designed regulated power supply can compensate for it's internal source resistance and provide an effective equivalent of a zero source resistance, but that is as close as you can get, and it is not simple.
 

Audioguru again

Joined Oct 21, 2019
1,908
The 9V alkaline battery used in my smoke detector produces 8V with a current of 100mA when new. After being used for 1 year its voltage drops to 6V when its current is only 15mA.
Therefore its internal resistance is (9V - 8V)/100mA= 10 ohms and its internal resistance after 1 year is (9V - 6V)/15mA= 200 ohms.
 

WBahn

Joined Mar 31, 2012
26,143
The 9V alkaline battery used in my smoke detector produces 8V with a current of 100mA when new. After being used for 1 year its voltage drops to 6V when its current is only 15mA.
Therefore its internal resistance is (9V - 8V)/100mA= 10 ohms and its internal resistance after 1 year is (9V - 6V)/15mA= 200 ohms.
What is it's open-circuit voltage after one year?
 

Audioguru again

Joined Oct 21, 2019
1,908
An Energizer 9V alkaline battery has a guaranteed 5 years shelf life. After only one year its open circuit voltage is 9V.
A Chinese Super-Heavy-Duty 9V battery has no guarantee and is seen leaking in its package in the store after a couple of weeks in the boat.
 

MisterBill2

Joined Jan 23, 2018
6,998
An Energizer 9V alkaline battery has a guaranteed 5 years shelf life. After only one year its open circuit voltage is 9V.
A Chinese Super-Heavy-Duty 9V battery has no guarantee and is seen leaking in its package in the store after a couple of weeks in the boat.
"Heavy Duty" in a battery name means it is able to deliver more current for a while. Sort of the opposite of long life. And of course there are always the really poor quality batteries that will leak and give other sorts of grief even before you buy them.
 

WBahn

Joined Mar 31, 2012
26,143
An Energizer 9V alkaline battery has a guaranteed 5 years shelf life. After only one year its open circuit voltage is 9V.
A Chinese Super-Heavy-Duty 9V battery has no guarantee and is seen leaking in its package in the store after a couple of weeks in the boat.
But you were talking about a battery that had been in use for a year, not sitting in a package on the shelf.
 
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