Who found out the relationship between the current I flowing in a metallic wire and the potential difference across its terminals?

Georg Simon Ohm

The correct answer is option 2. Georg Simon Ohm.

Georg Simon Ohm, a German physicist, established the fundamental relationship between the electric current flowing through a conductor and the potential difference applied across its terminals. This relationship, known as Ohm's Law, is one of the fundamental principles of electricity and forms the basis of many electrical theories and applications.

Ohm's Law states that the electric current (I) flowing through a conductor is directly proportional to the potential difference (V) applied across its ends, provided that the temperature and other physical conditions remain constant. Mathematically, Ohm's Law is represented as:

\[ V = IR \]

Where:

\( V \) is the potential difference (voltage) across the conductor in volts (V),

\( I \) is the electric current flowing through the conductor in amperes (A),

\( R \) is the resistance of the conductor in ohms (Ω).

This relationship implies that if the potential difference across a conductor increases, the current flowing through it also increases proportionally, given that the resistance remains constant. Similarly, if the potential difference decreases, the current decreases accordingly.

Ohm's Law is fundamental in understanding and analyzing various electrical circuits, including circuits in electronics, power systems, and telecommunications. It enables engineers and scientists to predict and control the behavior of electrical systems, design circuits, and troubleshoot problems effectively.