The resistance of a conductor is inversely proportional to:
Area of cross section
Understanding Conductor Resistance
The resistance of a conductor is a measure of how much it opposes the flow of electric current. This property depends on several factors related to the material the conductor is made of and its physical dimensions.
Factors Affecting Resistance
The resistance (\(R\)) of a uniform conductor is described by the formula:
\[R = \frac{\rho L}{A}\]
Where:
- \(R\) is the resistance of the conductor.
- \(\rho\) (rho) is the resistivity of the material. This is an intrinsic property of the material itself.
- \(L\) is the length of the conductor.
- \(A\) is the cross-sectional area of the conductor.
Let's analyze how resistance is proportional to each factor:
- Resistivity (\(\rho\)): From the formula, \(R\) is directly proportional to \(\rho\). If the resistivity of the material increases, the resistance increases. Different materials have different resistivities.
- Length (\(L\)): From the formula, \(R\) is directly proportional to \(L\). A longer conductor offers more resistance to the flow of current than a shorter one of the same material and thickness.
- Area of cross section (\(A\)): From the formula, \(R\) is inversely proportional to \(A\). This means that if the cross-sectional area increases, the resistance decreases. A thicker wire (larger area) offers less resistance than a thinner wire (smaller area) of the same material and length.
Resistance also depends on Temperature. For most metallic conductors, resistance increases as temperature increases. This is because increased thermal vibrations of the atoms hinder the flow of electrons more. However, this relationship is not a simple inverse proportionality in the form of the basic resistance formula.
Analyzing the Options
We are looking for the factor to which resistance is inversely proportional.
- Temperature: Resistance typically increases with temperature for conductors (direct, not inverse, relationship, though more complex than linear).
- Resistivity: Resistance is directly proportional to resistivity (\(R \propto \rho\)).
- Area of cross section: Resistance is inversely proportional to the area of cross section (\(R \propto \frac{1}{A}\)).
- Length: Resistance is directly proportional to length (\(R \propto L\)).
Based on the formula and the analysis of the options, resistance is inversely proportional to the area of cross section.
| Factor | Relationship with Resistance | Proportionality |
|---|---|---|
| Resistivity (\(\rho\)) | \(R \propto \rho\) | Directly Proportional |
| Length (\(L\)) | \(R \propto L\) | Directly Proportional |
| Area of cross section (\(A\)) | \(R \propto \frac{1}{A}\) | Inversely Proportional |
| Temperature | Generally \(R\) increases with \(T\) for conductors | Generally Direct (not simple inverse) |
Conclusion
The resistance of a conductor is inversely proportional to its area of cross section. A larger cross-sectional area means more space for electrons to flow, thus reducing resistance.
Revision Table: Conductor Resistance Factors
| Factor | Influence on Resistance | Relationship |
|---|---|---|
| Material (Resistivity) | Higher resistivity means higher resistance | Direct |
| Length | Longer length means higher resistance | Direct |
| Area of Cross Section | Larger area means lower resistance | Inverse |
| Temperature | Higher temperature typically means higher resistance (for metals) | Direct (generally) |
Additional Information on Resistance
The concept of resistance is fundamental in electrical circuits. It dictates how much current flows for a given voltage, according to Ohm's Law (\(V = IR\)). Understanding the factors that influence resistance is crucial for designing and analyzing electrical systems. For instance, power transmission lines use thick cables (large area of cross section) made of materials like copper or aluminum (low resistivity) to minimize resistance and reduce power loss due to heating (\(P = I^2R\)). Temperature effects are also important, especially in sensitive electronic components or when conductors operate under varying thermal conditions.
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