EMF and
Terminal Voltage
Emf = Useful volts + Lost volts
In code:
ℇ
= V + v
We can represent the circuit with internal resistance as:
So our cell is now a:
perfect battery in series with an internal resistor, r.
We can now treat this as
a simple series circuit and we know that the current, I,
will be the same throughout the circuit. We also know the
voltages in a series circuit add up to the battery voltage.
Emf = voltage across R
+ voltage across the internal resistance
ℇ
=
V + v
We also know from Ohm’s
Law that:
V = IR
and
v = Ir
so we can write:
ℇ
= IR + Ir
Many students panic at
the sight of internal resistance problems. All you have to do is turn
the cell with the internal resistance into a
perfect battery in series with its internal resistor,
and treat it as a
simple series circuit.
In experiments to determine the internal resistance, we
get a graph like this:
The graph is a straight
line, of the form y = mx + c.
We can make the equation
for internal resistance:
V = rI + E
There are three features
on the graph that are useful:

The intercept
on the yaxis tells as the emf.

The intercept
on the xaxis tells us the maximum current the cell
can deliver when the p.d. is zero, i.e. a dead short circuit.

The negative
gradient tells us the internal resistance.
