Electrical engineers sometimes use a wire's conductance, G=σA/L, instead of its resistance. What is the conductance of a 5.4-cm-long, 0.15-mm-diameter tungsten wire?

Verified step by step guidance

1. Understand the formula for conductance: \( G = \frac{\sigma A}{L} \), where \( \sigma \) is the conductivity of the material, \( A \) is the cross-sectional area of the wire, and \( L \) is the length of the wire.
2. Convert the given dimensions into SI units: The length \( L \) is given as 5.4 cm, which is \( 0.054 \, \text{m} \). The diameter of the wire is 0.15 mm, which is \( 0.00015 \, \text{m} \).
3. Calculate the cross-sectional area \( A \) of the wire, assuming it is circular: \( A = \pi r^2 \), where \( r \) is the radius of the wire. The radius is half the diameter, so \( r = \frac{0.00015}{2} \, \text{m} \). Substitute this value into the formula for \( A \).
4. Look up the conductivity \( \sigma \) of tungsten. For tungsten, \( \sigma \) is approximately \( 1.79 \times 10^7 \; \text{S/m} \). Substitute this value, along with \( A \) and \( L \), into the conductance formula \( G = \frac{\sigma A}{L} \).
5. Simplify the expression to find the conductance \( G \). Ensure all units are consistent (e.g., meters for length and square meters for area) to obtain the result in Siemens (S).

Key Concepts

Conductance

Conductance is a measure of how easily electric current can flow through a material. It is the reciprocal of resistance and is defined by the formula G = σA/L, where G is conductance, σ is the material's conductivity, A is the cross-sectional area, and L is the length of the conductor. Higher conductance indicates a better ability to conduct electricity.

Cross-sectional Area

The cross-sectional area (A) of a wire is the area of a slice taken perpendicular to its length. For a cylindrical wire, it can be calculated using the formula A = π(d/2)², where d is the diameter. This area is crucial in determining the conductance, as a larger area allows more current to pass through.

Material Conductivity

Material conductivity (σ) is a property that quantifies how well a material can conduct electric current. Different materials have different conductivity values, with metals like tungsten having high conductivity. This property is essential in calculating conductance, as it directly influences how easily current can flow through the wire.