A square film of Nichrome (an alloy of nickel and chromium) is deposited on a sheet of glass, and copper electrodes are then deposited on two opposite edges. Show that the resistance between the electrodes depends only on the thickness of the film and on its conductivity, as long as the film is square. This resistance is given in ohms per square. Nichrome films range approximately from 40 to 400 ohms per square.

Conductivity is a fundamental property of materials that describes their ability to conduct electric current. It is the inverse of resistivity, denoted as \( \sigma \), and is measured in units of siemens per meter (S/m). Conductivity is affected by the material's elemental composition, temperature, and the presence of impurities or defects.

For instance, metals like copper and silver have high conductivity due to the free movement of their valence electrons, making them excellent conductors. In contrast, insulators like rubber have very low conductivity, as their electrons are tightly bound and not free to move. In the exercise's case of the Nichrome film, knowing its conductivity is crucial for calculating the resistance offered when a voltage is applied between the copper electrodes.

Resistivity, symbolized by \( \rho \), is the measure of how strongly a material opposes the flow of electric current. It is the reciprocal of conductivity and is typically measured in ohm-meters (\(\Omega \cdot m\)). Factors such as temperature, material structure, and the presence of impurities can significantly influence resistivity.

Materials with low resistivity are known as conductors as they allow current to pass through easily, while those with high resistivity are called insulators. The relationship between resistivity and resistance is highlighted in the Nichrome film example where the resistance \( R \) is directly proportional to resistivity \( \rho \) and inversely proportional to the cross-sectional area \( A \) of the film. Since our exercise deals with a square shape, the dimensions simplify the formula, as both the length and width contribute equally to the area through which current flows.

Ohm's Law is a foundational principle in the field of electricity, which states that the current \( I \) through a conductor between two points is directly proportional to the voltage \( V \) across the two points and inversely proportional to the resistance \( R \) of the conductor. The law is expressed with the formula: \[ I = \frac{V}{R} \]

Ohm's Law enables us to calculate how much current will flow through a circuit for a given voltage and resistance. This principle underlies many practical applications in electronics and electrical engineering. Understanding how resistance is determined by material properties, like in the Nichrome film example, helps us use Ohm's Law to predict how electrical circuits will behave under various conditions and with differing materials.