Terminal Voltage

Many persons get confused when given problems to solve for the terminal voltage or pd in a circuit mostly because it sounds the same as the E.M.F / total voltage of the circuit and so often loses a point or the entire question for this error. Here we will distinguish between the e.m.f and terminal voltage or p.d of a cell and show you examples of terminal voltage.

What is E.M.F?
E.m.f or electromotive force is the work or energy per unit charge that an active current producing device produces to drive current through a circuit.
In simpler terms a source that produces its own voltage has e.m.f.

What is Terminal Voltage?
Terminal voltage is the voltage / potential difference across the terminals of a cell or battery.

If the cell/battery is not connected to circuit then the terminal voltage/p.d is equal to the e.m.f of the cell or battery.
If the cell or battery is connected to a circuit then the terminal voltage/p.d is equal to the total voltage drop in the external circuit.

Cell/Battery not connected to a Circuit

Terminal P.D = E.M.F

Cell/Battery connected to a Circuit

Formula for Terminal Voltage when connected to a circuit:
EMF = v +V
EMF = Ir + IR
Therefore:
Terminal P.D = IR

Where:
v is voltage within the cell
V s voltage in external circuit
r is internal resistance
R is resistance in external circuit

I is current 

Don’t be fooled into thinking the terminal P.d would be Ir by looking at the diagram above the terminal voltage is the same as the voltage in external circuit in this case, this is because the cell is connected to a circuit and not by itself as is the case with the first diagram.