EMF Khan Academy- Understanding Electromotive Force

What EMF Actually Is (It's Not What You Think)

Here's the bitter truth: electromotive force is not a force. The name is a historical accident that stuck around long after physicists realized it was misleading.

EMF is energy per unit charge. It's measured in volts, just like potential difference. The confusion exists because early scientists thought EMF was some kind of "force" that pushed electrons through a circuit. We now know better, but the name never changed.

The Real Definition

EMF (symbol: ℰ) is the energy provided by a voltage source per coulomb of charge. When you have a 9V battery, it delivers 9 joules of energy to every coulomb of charge that flows through it.

Think of EMF as the maximum potential difference a source can create between its terminals when no current flows. Once you connect a load and current starts moving, things change.

How Voltage Sources Actually Work

A voltage source like a battery or generator maintains a potential difference. It does this through chemical reactions (batteries) or electromagnetic induction (generators).

Inside a battery, chemical reactions separate charges. One terminal accumulates positive charge, the other negative. This separation creates the EMF. The battery essentially pumps charges from the low-potential terminal to the high-potential terminal, fighting against the internal forces that would equalize the charge.

Simple Circuit Breakdown

Here's what happens in a basic circuit:

The voltage source creates EMF (ℰ)
Charge flows from the positive terminal through the external circuit
The charge does work on components (lights, resistors, motors)
Charge returns to the negative terminal
The battery's chemical processes restore the charge separation

EMF vs Terminal Voltage: The Critical Difference

This is where most students get tripped up. EMF is not the same as the voltage you measure across a battery's terminals when it's connected to a circuit.

When current flows, internal resistance (r) inside the battery causes a voltage drop. The terminal voltage (V) is always less than the EMF:

V = ℰ - Ir

Where:

V = terminal voltage (what you measure with a voltmeter)
ℰ = EMF of the source
I = current flowing through the circuit
r = internal resistance of the source

Why This Matters

A fresh 9V battery might actually read 9.5V when you check it with a multimeter (no load). Connect it to a circuit drawing significant current, and the terminal voltage drops. The battery is "weaker" not because it's depleted, but because internal resistance increases as chemical reactants get used up.

Comparing EMF, Terminal Voltage, and Potential Difference

Concept	Symbol	Measured When	What It Represents
EMF	ℰ	No current flowing (open circuit)	Energy per charge provided by source
Terminal Voltage	V	Current flowing (closed circuit)	Actual voltage across source terminals
Potential Difference	ΔV	Across any two points	Work done per unit charge between points

Internal Resistance: The Hidden Culprit

Every real voltage source has internal resistance. It's not a physical resistor sitting inside the battery—it's an effect of the source's construction and chemistry.

Sources with low internal resistance can deliver high currents without significant voltage drop. car batteries have very low internal resistance (around 0.001-0.005 Ω), which is why they can deliver hundreds of amps to start a starter motor.

What Affects Internal Resistance?

Battery age — internal resistance increases as chemicals deplete
Temperature — higher temps usually mean lower internal resistance
Current magnitude — some batteries show increased resistance at high currents
Physical size and design — larger electrodes and more electrolyte generally mean lower resistance

How to Calculate EMF Problems

Basic Setup

Most EMF problems involve finding one of four things: EMF, terminal voltage, current, or internal resistance. The key equation is:

ℰ = V + Ir

Or rearranged for terminal voltage:

V = ℰ - Ir

Step-by-Step Example

Problem: A battery with EMF of 12V and internal resistance of 0.5Ω is connected to a circuit drawing 2A. What is the terminal voltage?

Identify known values: ℰ = 12V, r = 0.5Ω, I = 2A
Apply the formula: V = ℰ - Ir
Calculate the internal drop: Ir = 2A × 0.5Ω = 1V
Find terminal voltage: V = 12V - 1V = 11V

Finding Internal Resistance

Problem: A battery reads 13.5V when open-circuited and 12V when delivering 3A. Find internal resistance.

EMF equals open-circuit voltage: ℰ = 13.5V
Use V = ℰ - Ir: 12V = 13.5V - (3A × r)
Solve: 3A × r = 1.5V, so r = 1.5V / 3A = 0.5Ω

Series and Parallel Voltage Sources

When you connect voltage sources together, their EMFs add (series) or their internal resistances combine differently (parallel).

Series Connection

Total EMF: ℰ_total = ℰ₁ + ℰ₂ + ℰ₃...

Total internal resistance: r_total = r₁ + r₂ + r₃...

Two 1.5V batteries in series give you 3V. Simple.

Parallel Connection

Total EMF: Same as one source (assuming identical sources)

Total internal resistance: 1/r_total = 1/r₁ + 1/r₂ + ...

Parallel connection doesn't increase voltage. It decreases effective internal resistance, allowing the circuit to draw more current without voltage drop.

Real-World EMF Applications

Solar cells — EMF depends on cell material and light intensity
Thermocouples — EMF generated by temperature differences between junctions
Generators — EMF produced through magnetic flux changes
Fuel cells — EMF from electrochemical reactions (similar to batteries)

Common Mistakes to Avoid

Confusing EMF with voltage — They're numerically similar but conceptually different. EMF is the cause; terminal voltage is the effect.
Ignoring internal resistance — Real circuits always have it. Pretending they don't gives wrong answers.
Forgetting the current direction — The internal resistance drop subtracts from EMF. Current leaving the positive terminal causes this drop.
Assuming ideal sources — No real voltage source has zero internal resistance. Every battery, generator, and power supply has losses.

The Bottom Line

EMF is energy per unit charge that a source can provide. It exists whether or not current flows. Once current flows, internal resistance causes a voltage drop, and the terminal voltage becomes less than the EMF.

For any circuit analysis problem, start with ℰ = V + Ir and identify what you're solving for. The math is straightforward once you understand what each term represents.