# E.m.f and Potential Difference ## Understanding Potential Difference - When a cell is connected to a circuit, one terminal becomes positive while the other becomes negative - This creates a **potential difference** (p.d.) between different points in the circuit

Potential difference is the energy transferred per unit charge as current flows from one point to another in a circuit

- The unit of p.d. is the **volt** (V), which is equivalent to joules per coulomb ($\text{J C}^{-1}$) - Think of it this way: if a lamp has a p.d. of 6 V across it, each coulomb of charge delivers 6 J of energy to the lamp - Energy is transformed from electrical energy into other forms (e.g., light, heat, kinetic energy) ## P.D. Across Series Components - When components are connected in series with a power supply, the total p.d. is divided among all components - The sum of individual p.d. values across each component equals the supply voltage - For example: a 9 V battery with three resistors in series might have p.d. values of 2 V, 3 V, and 4 V across the three resistors respectively | Component | Potential Difference | |-----------|---------------------| | Resistor 1 | 2 V | | Resistor 2 | 3 V | | Resistor 3 | 4 V | | **Total** | **9 V** | - The chart below visualizes how the supply voltage is distributed across the series components:

- Notice how the individual voltages (2 V + 3 V + 4 V) add up to equal the total supply voltage (9 V) ## Measuring Potential Difference - P.D. is measured using a **voltmeter** - The voltmeter must be connected in **parallel** with the component being measured - This allows the voltmeter to measure the energy difference between two points without significantly affecting current flow ## Comparing E.M.F. and Potential Difference

E.m.f. and p.d. differ in the direction of energy transfer per unit charge

### Potential Difference (p.d.) - Represents the **loss** or **dissipation** of electrical energy by charges - Electrical energy is **converted** into other forms (thermal, light, sound, etc.) - For instance, when charge flows through a heater: - Electrons lose electrical potential energy - This energy is transformed into thermal energy - The heater has a p.d. across it equal to the energy dissipated per coulomb ### Electromotive Force (e.m.f.) - Represents the **gain** or **supply** of energy to electrical charges - Energy from chemical reactions (in batteries) or mechanical work (in generators) is **transferred** to electrical charges - For example, in a battery: - Chemical energy is converted to electrical energy - Each coulomb of charge gains energy as it passes through the battery - The e.m.f. equals the energy supplied per coulomb ## Energy Transfer Equations - Both e.m.f. and p.d. relate to energy transfer, expressed by similar equations: $$W = VQ$$ - Where: - $W$ = work done or energy transferred (J) - $V$ = potential difference (V) - $Q$ = charge (C) - For e.m.f., this can be written as: $$W = \varepsilon Q$$ - Where: - $\varepsilon$ = electromotive force (V) - The relationship between energy transferred and charge is linear - doubling the charge doubles the energy transferred for a given voltage

- The graph shows how energy transfer varies with charge for different voltages (3 V, 6 V, and 9 V) - Higher voltages result in greater energy transfer per coulomb (steeper gradients)

Voltage and p.d. are the same concept, but e.m.f. is different—it describes energy supplied to charges, not dissipated by them

## Key Distinctions Summary | Property | Potential Difference | E.M.F. | |----------|---------------------|--------| | **Energy direction** | Energy lost by charges | Energy gained by charges | | **Energy transformation** | Electrical → other forms | Other forms → electrical | | **Where it occurs** | Across components (resistors, bulbs) | Across power supplies (cells, batteries) | | **Equation** | $W = VQ$ | $W = \varepsilon Q$ | | **Units** | Volts (V) or $\text{J C}^{-1}$ | Volts (V) or $\text{J C}^{-1}$ |