Terminal Voltage

Question

A 1.5 V source has internal resistance of 1.0 Ω. What current must flow through the cell so that the terminal voltage is equal to the EMF?

Answer 1

Hi Jamie!

 

The way the question is written, it sounds like a bit of a trick.  Batteries are created with a certain potential difference across their electrochemical core, and a bunch of charges (stored at that potential) which can then run off into a circuit and deliver their electrical potential energy to some device or other.  When we say a battery is "1.5 V," as above (with no modifiers or extra information), we usually mean the potential difference inside its core, where the charges are stored.  This is what is typically called the battery EMF (or electromotive force, an old term that basically means the same thing as potential difference or voltage, but can be used to signify particular *kinds* of potential difference, such as those in the core of a battery).

 

However, to get the charges stored in the battery core out to the rest of the circuit (and back to the core once they have left the circuit) requires running them through short stretches of wire to get to a point where the outside circuit can hook on.  These "hook-on" points are the terminals of the battery.  However, the short bits of wire connecting the core to the battery inside have a tiny amount of resistance of their own, and so the charges lose some electrical potential energy just traveling to the terminals.  This causes some of the core voltage to be dropped *inside* the battery.  So, by the time you get to the terminals in the battery, the voltage is already a touch lower than it was in the core (the battery EMF).  This is the "terminal voltage," the potential difference the battery delivers to the rest of the circuit.

 

Any flow of charge through the interior wiring of the battery causes this drop in voltage that makes the terminal voltage lower than the EMF, because as soon as the charge flows through the internal wiring, it experiences that resistance and the corresponding drop in potential.

 

As a result, the only current that would make the terminal voltage exactly equal to the battery EMF is a (net) current of zero.  Any non-zero (net) current must make the terminal voltage different from the battery EMF.

 

I will think about this more and see if I am missing something, But I hope this still has a chance to help some!  Let me know if you have any more questions or have further information that modifies the problem.

 

 

Answer 2

Use ohm's law.  The EMF voltage is the same as the source voltage.

 

EMF_voltage = voltage source

 

I = V / R

 

where:

V = 1.5 V

R = 1 Ω