Question

A cylindrical conductor of length 1 and uniform area of cross section A has resistance R. Another conductor of same material and resistance R has length 21. what will be it's area of cross section ​

Answer 1

Answer: area of cross section will be 2A

Hi Aashritha , this is Anu (actually it is not 1 it is L , so kindly replace the 1s with Ls) and check the answer below

The resistance of a wire is

R=ρ  A/L

which can also be represented as

A=ρ  R/L

 

   

where,

ρ - Resistivity

L - Length

A - Area of a cross-section

◇ WKT, the length is directly proportional to the resistance and the area of cross-section is inversely proportional to the resistance.

◇ In this case, the length of the conductor is doubled (2L) and so the resistance will be 2R. For the resistance to remain the same as R, the area of cross-section is also doubled as 2A.

therefore, the area of cross-section is 2A.

Answer 2

Answer:

Step 1: Evaluation of resistance of the first conductor in terms of resistivity.

We know that,

R=ρ

A

L

ρ is the resistivity of the cylindrical conductor.

Step 2: Evaluation of resistance of the second conductor in terms of resistivity.

We know that,

R

′

=ρ

A

′

2L

A

′

is the unknown cross section of the second conductor.

Step 3: Comparing the two expressions

Since R

′

=R (Given)

or, ρ

A

L

=ρ

A

′

2L

A

′

=2A

Final Step : The second conductor of length 2L and resistance R has an area of 2A