A material of length L and area of cross section has a resistance R . What should be changes in the area of cross section A if its length is tripled to produce the same resistance ?

Correct option is C

The correct answer is (c) The area of cross section should be increased by 3 times.

Solution: 

​The resistance $R$ of a material is given by the formula:

$$R = \rho \frac{L}{A}$$

where:

• $R$ = Resistance
• $\rho$ = Resistivity
• $L$ = Length
• $A$ = Area of cross section 
• $$L' = 3L$$

When the length is tripled, the new length L′=3LL' = 3L $$L' = 3L$$​. To maintain the same resistance, the formula becomes:​

$$R' = \rho \frac{3L}{A'}$$

For the resistance to remain the same, we equate R=R′R = R' $$R = R'$$ , so:

$$\rho \frac{L}{A} = \rho \frac{3L}{A'}$$

Simplifying this, we get:
                                                       $$A' = 3A$$

Therefore, to maintain the same resistance, the area of cross section must be increased by 3 times, which corresponds to option (C).

Information Booster:

• Resistance Formula: Resistance $R$ is directly proportional to the length $L$ and inversely proportional to the area of cross section $A$.
• Effect of Length: Tripling the length of a material increases the resistance unless the area of cross section is adjusted.
• Inverse Relation: To maintain constant resistance, increasing the length requires increasing the area of cross section.
• Final Answer: The area must be increased by 3 times to keep the resistance constant when the length is tripled.

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