Electromotive Force and Electric Circuits
Simple Explanation
A battery's electromotive force (EMF, Ξ΅) is the total energy it supplies per unit charge β but a real battery also has internal resistance, so the actual voltage available to a circuit (terminal voltage) is always a little less than the full EMF: V=Ξ΅βIr.
Why Do We Need It?
Understanding EMF and internal resistance explains why a battery's voltage seems to "sag" under heavy load β a genuinely practical fact about every real power source, from AA batteries to car batteries.
See It
A rectangular circuit loop with a battery (EMF Ξ΅ and internal resistance r) on the left side and a resistor R on the right side, with an arrow showing the direction of current flow
Formula
Terminal Voltage of a Battery
V = Ξ΅ β Ir
A real battery's terminal voltage (what a circuit actually sees) is always slightly less than its full EMF, because some voltage is lost driving current through the battery's own internal resistance.
- V
- β terminal voltage, in volts (V)
- Ξ΅
- β electromotive force (EMF) of the battery, in volts (V)
- I
- β current flowing through the circuit, in amperes (A)
- r
- β the battery's internal resistance, in ohms (Ξ©)
When to use it: Whenever the actual voltage a circuit experiences (as opposed to the battery's ideal EMF) needs to be found, accounting for internal resistance.
Worked Example
Find a battery's terminal voltage
A battery has EMF 12 V and internal resistance 0.5 Ξ©. When it drives 2 A through a circuit, find its terminal voltage.
Why Does This Work?
Some of the energy the battery supplies must be used to push current through its own internal resistance β by Ohm's law, that "lost" voltage is Ir, so what remains available at the terminals for the rest of the circuit is Ξ΅ minus that internal voltage drop.
Real-Life Example
A car battery's voltage dropping while starting the engine
A car battery's voltage visibly dips for a moment while the starter motor draws a very large current to crank the engine.
That large starting current (I) flowing through the battery's own internal resistance (r) causes a significant voltage drop (Ir), temporarily reducing the terminal voltage below the battery's full EMF.
Practice
A battery has EMF 9 V and internal resistance 0.3 Ξ©. Find its terminal voltage when it drives 3 A through a circuit.
MediumCommon mistake
Assuming a battery always supplies exactly its rated EMF to a circuit β the actual terminal voltage is always somewhat lower once current flows, due to the unavoidable internal resistance.
Quick Review
- V = Ξ΅ β Ir.
- EMF is the battery's total energy per unit charge; terminal voltage is what the circuit actually gets.
- Terminal voltage drops further under heavier current draw.