If the resistance decreases does the terminal voltage change?

Question

The terminal voltage V is equal to E - Ir where r is the internal resistance. Suppose the battery is connected to a resistor with resistance R. If R is changed does the terminal voltage change?

I know that the voltage of the battery is not supposed to be affected but then again if R changes then I changes too and V = E - Ir where E and r are constant. I changes so shouldn't V change too?

Answer 1

Yes, for a 'real' battery, the terminal voltage changes - it drops as the current in the circuit increases.



At an introductory level ,students are often taught that a battery provides a constant voltage whatever is connected to it. This is an 'ideal' battery which has no internal resistance and can deliver an unlimited current. This is OK for introductory teaching purposes though students sometimes spot the weakness.



At a more advanced level the effect if internal resistance is taught. V reduces as I increases.

The quantity Ir is sometimes called the 'lost volts'. In the extreme case of short-circuiting the battery (zero resistance between the terminals) the lost volts equals the emf and the terminal voltage becomes zero. So internal resistance is very important when considering 'real' batteries.



At an even more advance level you find that emf and internal resistance are only approximately constant and depend in a complex way on the history of the battery's usage.

Answer 2

Good observation.



I would guess that the current increasing would mean that the voltage does indeed change, but internal resistances are usually very very small compared to the load ohms...ie. negligible . So your current can never be large enough to see an effect if the internal resistance is small enough.



I would guess that, if your internal resistance were large enough then E -Ir =0 ie...E =Ir in that case you have just defined the maximum current possible through the circuit. In reality even the wire(conductor) has a resistance, therefore the current will never reach that maximum limit.



Heres a good source for you:



http://www.ece.utah.edu/~harrison/lpdocs/lecture1.pdf

Answer 3

Yes .. the terminal pd changes as the current changes.



It's the emf and internal resistance that are usually constant.



V = E - ir ..as the current increases so does the 'lost' pd across the internal resistance (ir) .. with the external (terminal) pd (V) decreasing by this amount (ir).



The internal (lost) pd produces the internal heating (i²r) of the emf source.