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In electric circuits, Ohm's Law is an easy yet powerful tool used to determine how voltage, current, and resistance relate to each other. The law is formulated as: \( V = I \cdot R \), where:

• \( V \) is the voltage in volts (V),
• \( I \) is the current in amperes (A), and
• \( R \) is the resistance in ohms (Ω).

This means the voltage across a conductor is directly proportional to the current flowing through it and the resistance of the conductor.
For example, in our exercise involving a car battery and headlights, Ohm’s Law was used to find the current when only the headlights were powered. The formula used was \( I = \frac{V}{R} \), where the total resistance included both the headlights and the internal resistance of the battery. This provided the current flowing through the circuit, leading to further calculations.

Electromotive force, often abbreviated as emf, is like the energy supply of a battery. It’s measured in volts and can be thought of as the "pressure" that pushes the electrical current around the circuit. Though termed as a force, it is actually not a force but a potential difference. It represents the total voltage the battery can supply when no current flows.
In our car battery example, the emf is given as \( 12.6 \mathrm{~V} \). This is the theoretical voltage available when nothing is connected to the battery yet. Once a load, like the headlights or the starter motor, is connected, the real voltage across the terminals might be less because of internal resistance causing voltage drop.

When you deal with real-world batteries, you can't ignore internal resistance, which is the resistance within the battery that opposes the flow of current. It plays a crucial role in determining how much voltage is available at the terminals of a battery when a current is flowing.
For instance, in the provided problem, the internal resistance of the car battery is \(0.080 \Omega\). This resistance causes some of the emf to be "used up" just to get the current through the battery itself before it even reaches the external circuit, such as the headlights. The effect becomes more noticeable when high currents are drawn, like when starting the car, leading to a lower potential difference across the components in the circuit.