Question

Resistance of a conductor depends on :

• A. length
• B. area of cross section
• C. material
• D. all the above

Hint:

The resistance (\(R\)) of a conductor is determined by: 1. {Length (\(L\)):} Longer wire \(\rightarrow\) More resistance (\(R \propto L\)). 2. {Area of cross-section (\(A\)):} Thicker wire (larger A) \(\rightarrow\) Less resistance (\(R \propto 1/A\)). 3. {Material (Resistivity \(\rho\)):} Different materials have different intrinsic abilities to resist current flow (\(R \propto \rho\)). 4. {Temperature:} For most conductors, resistance increases with temperature. The formula combining the first three is \(R = \rho \frac{L}{A}\). Since options (1), (2), and (3) are all factors, "all the above" is correct.

Answer 1

The Correct Option is D

Concept: The electrical resistance (\(R\)) of a conductor is a measure of its opposition to the flow of electric current. Several factors influence this resistance. Step 1: Factors affecting the resistance of a conductor The resistance of a conductor is given by the formula: \[ R = \rho \frac{L}{A} \] where:
\(R\) is the resistance.
\(\rho\) (rho) is the resistivity (or specific resistance) of the material of the conductor. Resistivity is an intrinsic property of the material itself (e.g., copper has low resistivity, nichrome has higher resistivity).
\(L\) is the length of the conductor. Resistance is directly proportional to the length; longer conductors offer more resistance.
\(A\) is the area of cross-section of the conductor. Resistance is inversely proportional to the cross-sectional area; thicker wires (larger area) offer less resistance. Additionally, the resistance of most materials also depends on temperature. For most conductors, resistance increases with increasing temperature. Step 2: Analyzing the options
(1) length (\(L\)): Yes, resistance is directly proportional to length (\(R \propto L\)).
(2) area of cross section (\(A\)): Yes, resistance is inversely proportional to the area of cross-section (\(R \propto 1/A\)).
(3) material (\(\rho\)): Yes, the resistivity (\(\rho\)) is a property of the material, and resistance depends on resistivity. Different materials have different resistivities.
(4) all the above: Since resistance depends on length, area of cross-section, and the material (which determines resistivity), this option is correct. (Temperature is another factor, but it's not among the options here). Therefore, the resistance of a conductor depends on its length, area of cross-section, and the material it is made of.