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Electromotive Force (EMF) is the term used to describe the voltage generated by a battery or power source when no current is flowing. It is essentially the ideal voltage that the battery can provide, as if it had no internal resistance.

In practical terms, the EMF is the total potential difference across a power source when the current is zero. You can think of it as the peak ability of the battery to cause a current to flow through an external circuit.

The EMF, denoted as \( \mathcal{E} \), is measured in volts (V). It is not influenced by the actual flow of electrons within the battery but represents the battery's open-circuit voltage.

• The EMF of a battery remains constant when the battery is not discharging or charging any load.
• It differs from the measured terminal voltage because of the energy losses associated with the internal resistance of the battery.

To determine the EMF, we rely on other electrical equations, like Ohm's Law, and compensate for the battery's internal resistance.

Ohm's Law is a fundamental principle in electronics relating voltage, current, and resistance in a simple linear equation: \( V = IR \).

Here, \( V \) represents the voltage across a component, \( I \) is the current flowing through it, and \( R \) is its resistance. Ohm’s Law helps us predict how a device will behave under different voltages and currents, making it a crucial tool in both circuits analysis and design.

• This equation implies a direct proportionality: as the voltage across a component increases, the current through it also increases if the resistance remains constant.
• It's important to note that this law assumes the behavior of linear, ohmic materials where current is directly proportional to the applied voltage.

With real-world batteries, we apply Ohm's Law in a modified form to account for internal resistance, which can alter the effective voltage experienced across connected terminals.

Potential difference, often referred to simply as voltage, is the measure of the electrical potential energy per unit charge between two points in a circuit. It indicates how much energy is available to push the charges through the circuit.

This is measured in volts (V), the same unit as EMF, but unlike EMF, it directly depends on the current flowing and includes losses from internal resistance.

In our exercise, potential difference shifts with current changes; it was 8.4 V under one condition and 9.4 V under the other.

• This variance results from changes in internal voltage drops due to internal resistance in the battery.
• Potential difference across a battery's terminals is universally lower than the EMF when current flows in the battery's natural direction due to said internal resistance.

Understanding potential difference helps us recognize how much of the battery's stored energy is available for use in the circuit at any given moment.