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Terminal voltage is a crucial concept in the study of circuits and electronics. It refers to the voltage measured across the terminals of a power source when a load is connected. This voltage is what is effectively available for use by the external circuit. It is essential to understand that the terminal voltage of a battery or other voltage source will differ from its emf when there is a current flowing due to the presence of internal resistance.

The equation that describes this relationship is given by:
\( V = \text{emf} - I \cdot r \)
where \( V \) represents the terminal voltage, \( \text{emf} \) is the electromotive force, \( I \) is the current, and \( r \) is the internal resistance of the source.
In the context of the exercise, a drop in terminal voltage by 2.00 V when the current increases suggests that internal resistance is at play. By understanding how terminal voltage is influenced by current and internal resistance, it becomes possible to calculate the unknown internal resistance using these measured changes.

The term electromotive force, or emf, represents the energy provided by a power source per unit charge that passes through it. Although referred to as a 'force,' it is actually a potential difference measured in volts. Emf is the maximum voltage a power source can provide when no current is flowing, which means there is no voltage drop due to internal resistance. The emf can be thought of as the 'full' or 'ideal' voltage output of the source, before any internal factors, such as resistance, come into play.

To connect it to our original exercise, even though we can determine the internal resistance with the given information, we cannot ascertain the exact emf without knowing the initial terminal voltage or emf and the change in current. The equation involving emf, terminal voltage, and internal resistance is:
\( \text{emf} = V + I \cdot r \)
Understanding emf allows us to see the big picture of how power sources behave and influence the functioning of circuits.

Ohm's law is a fundamental principle in the field of electrical engineering and physics that relates current (\(I\)), voltage (\(V\)), and resistance (\(R\)) in a simple and direct manner. The law is mathematically represented as:
\( V = I \cdot R \)
This equation tells us that the voltage across a conductor is directly proportional to the current flowing through it, with the resistance being the factor of proportionality.

When it comes to internal resistance, Ohm’s law is modified to account for the voltage source itself, leading us to the formula:
\( \text{emf} = V + I \cdot r \)
Through this modified version, we see how the internal resistance of a voltage source affects the terminal voltage. In our original exercise, Ohm’s law helps us understand why there is a drop in terminal voltage with an increase in current and stands as the basis for calculating the internal resistance by relating the change in voltage to the change in current through the resistor.