Recall and use the equation for e.m.f. E = W / Q

4.2.3 Electromotive Force and Potential Difference ⚡️

What is Electromotive Force (e.m.f.)?

Think of a battery as a water pump that pushes electrons through a circuit. The e.m.f. is the push that moves the charge, just like the pump pushes water. It is measured in volts (V).

Potential Difference (Voltage) 🔋

Potential difference is the height difference that drives the electrons, similar to how a higher water level pushes water down. It is the energy per unit charge that the e.m.f. provides.

Key Equation

The e.m.f. is calculated by the work done on the charge divided by the charge moved:

$$E = \frac{W}{Q}$$

Where $W$ is the work in joules (J) and $Q$ is the charge in coulombs (C). The result is in volts (V) because 1 V = 1 J / 1 C.

Units and Conversion

Example Problem 💡

1. A battery does 15 J of work on the charges that flow through it. The total charge that passes is 3 C. What is the e.m.f. of the battery?
2. Use the equation: $E = \dfrac{W}{Q}$.
3. Plug in the values: $E = \dfrac{15\,\text{J}}{3\,\text{C}} = 5\,\text{V}$.
4. So the battery has an e.m.f. of 5 V.

Quick Recap 📌

• The e.m.f. is the energy supplied per unit charge.
• It is calculated with $E = \dfrac{W}{Q}$.
• Units: joules for work, coulombs for charge, volts for e.m.f.
• Think of e.m.f. as a pump and potential difference as the height difference that pushes electrons.