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The resistance R depends on...

The resistance R depends on

A

material of the conductor

B

dimension of conductor

C

Both (1)and(2)

D

Neither (1) nor (2)

Text Solution

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The correct Answer is:
To determine how the resistance \( R \) of a conductor depends on various factors, we can analyze the relationship using the formula for resistance. Here's a step-by-step solution: ### Step 1: Understand the Formula for Resistance The resistance \( R \) of a conductor is given by the formula: \[ R = \rho \frac{L}{A} \] where: - \( R \) is the resistance, - \( \rho \) is the resistivity of the material, - \( L \) is the length of the conductor, - \( A \) is the cross-sectional area of the conductor. ### Step 2: Identify the Factors Affecting Resistance From the formula, we can see that the resistance \( R \) depends on three main factors: 1. **Material of the Conductor**: The resistivity \( \rho \) is a property that depends on the material used. Different materials have different resistivities. For example, copper has a low resistivity and is a good conductor, while rubber has a high resistivity and is an insulator. 2. **Length of the Conductor**: The resistance is directly proportional to the length \( L \) of the conductor. This means that if the length increases, the resistance also increases. 3. **Cross-sectional Area of the Conductor**: The resistance is inversely proportional to the area \( A \) of the conductor. This means that if the area increases, the resistance decreases. ### Step 3: Conclusion Based on the analysis, we conclude that the resistance \( R \) depends on: - The material of the conductor (through resistivity \( \rho \)), - The length of the conductor \( L \), - The cross-sectional area of the conductor \( A \). Thus, the correct answer is that the resistance \( R \) depends on both the material and the dimensions (length and area) of the conductor. ### Final Answer The resistance \( R \) depends on: - The material of the conductor, - The length of the conductor, - The cross-sectional area of the conductor.
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