Question

A wire having resistance of 20 Ω length l and area of cross section A, is modified such that length is increased to 3 times and area of cross section is decreased to three times then what will be the effect on resistance.


60 Ω

6.667 Ω

Resistance will remain same

None of these
Please answer this question. ​

Answer 1

Answer:

Resistance, R=

A

ρl

When length l increases three times, the cross section A will decease three times of previous. So length becomes 3l and cross section becomes A/3.

Now resistance becomes ,R

′

=

πA/3

ρ3l

=9R=9×20=180Ω

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Answer 2

Answer:

(d) option is correct,None of these

Step by step Explanation:

Given:-

R(Resistance of wire)=20 Ω

l(Length of wire when increased to 3 times )=3×l

A(Area of cross section of wire when decreased to 3 times)=A/3

To find:-

R'(Resistance of wire after increase in length to 3 times and decrease in area of cross section to 3 times)

Solution:-

We know that,

R(Resistance)∝ l ----(1st equation)

                          A

R'(Resistivity of wire after increase in length to 3 times and decrease in area of cross section to 3 times)=>

R' ∝ 3×l

        A/3

R' ∝ 9× A    -------(2nd equation)

              l

From 1st and 2nd equation,we can say that there is 9 times change in resistance.

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