Resistance of a Wire

Resistance is a measure of how much a material opposes the flow of electric current. It depends on various factors such as the length, cross-sectional area, and resistivity of the wire. The formula for the resistance of a wire is:

R = (ρ * L) / A

where R is the resistance, ρ (rho) is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire.

Calculating Resistance

In this case, we are given the length of the wire as 3 meters and the cross-sectional area as 1.7 * 10^(-6) square meters. The resistance is given as 3 * 10 ohms.

Plugging these values into the formula, we get:

R = (ρ * 3) / (1.7 * 10^(-6)) = 3 * 10

We can rearrange the formula to solve for the resistivity:

ρ = (R * A) / L

Substituting the known values:

ρ = (3 * 10 * 1.7 * 10^(-6)) / 3 = 5 * 10^(-6) ohm-meter

Unit of Resistance

The unit of resistance is ohm (Ω), which is the SI unit for electrical resistance. It represents the ratio of voltage to current in a circuit. Resistance is a scalar quantity and can be measured using an ohmmeter.

Unit of Resistivity

The unit of resistivity is ohm-meter (Ω⋅m). It represents the inherent property of a material to resist the flow of electric current. Resistivity is a material-specific property and is used to compare the resistance of different materials of the same length and cross-sectional area.

Summary

To summarize, the formula for the resistance of a wire is R = (ρ * L) / A. Given the length, cross-sectional area, and resistance of the wire, we can calculate the resistivity using the formula ρ = (R * A) / L. The resistance is measured in ohms (Ω), while the resistivity is measured in ohm-meter (Ω⋅m).

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