Silver and iron wires of the same length and diameter carry the same current. How do the voltages across the two compare?

Electrical resistivity is a fundamental property that quantifies how strongly a material opposes the flow of electric current. A material with high resistivity means it has a tendency to resist the flow of electrons more than a material with low resistivity.

Take, for example, silver and iron. Silver has a low resistivity of approximately \(1.59 \times 10^{-8} \, \Omega \cdot m\), which means it allows electric current to pass through it very easily. Iron, on the other hand, has a higher resistivity of around \(9.71 \times 10^{-8} \, \Omega \cdot m\), making it less conductive.

Resistivity is important when comparing different materials for use in electrical applications. It's influenced by the type of material, its temperature, and its physical state. Knowing the resistivity of materials helps in designing circuits and electrical components that are efficient and effective.

Voltage calculation is a key element in understanding electrical circuits, as it allows us to determine the electric potential difference between two points. According to Ohm's Law, voltage \(V\) can be calculated using the formula: \(V = IR\), where \(I\) is the current and \(R\) is the resistance.

The application of this law is vital when analyzing circuits. In the case of the silver and iron wires carrying the same current, we can assert that any differences in the voltage across them are purely due to their resistances, which are in turn based on their resistivities and identical dimensions. Using Ohm's Law, you can predict the impact that changing one of the variables such as resistance or current will have on the voltage in a circuit.

When comparing the resistance of two different conductors, such as wires made of silver or iron, the comparison can tell us much about their ability to conduct electricity. Resistance, measured in ohms \(\Omega\), is directly proportional to the material's resistivity and the length of the conductor, and inversely proportional to its cross-sectional area.

In the context of this exercise, since the length and diameter of the silver and iron wires are the same, their resistances are influenced only by their material's resistivity. Silver's lower resistivity means it has a lower resistance compared to iron, which has a higher resistivity and consequently higher resistance.

Using the formula \(R = \frac{\rho L}{A}\), and knowing that the length \(L\) and cross-sectional area \(A\) are constant for both wires, it becomes clear that the wire made of silver will have a lower resistance than the wire made of iron. This is a valuable insight when designing circuits, as it guides the selection of materials based on the desired resistance properties.