Question

The resistance of conducting wire X of length 1 m is 5ohm calculate the resistance of the wire made by same material whose length is 4 times and area of cross-section is 5 times that of wire X (at same temperature)

Answer 1

Answer:

4Ω

Explanation:

R=ρl/A   ; where R is the resistance, ρ is the resistivity, l -length, A -area of cross-section

since both wire is made by one material, the ρ value will be same.

• for first wire, let the eqn be:

                  X=ρl/A  -----(a)

                           where X=5 Ω(given)

                                    l=1 m(given)

• for second wire, let the eqn be :

                  Y=ρl¹/A¹   --------(b)

                      where  l¹= 4l (given)  

                               A¹ = 5A (given)

• when we divide eqns (a) & (b), we get                                               $\frac{X}{Y}$ = l.A¹/l¹.A   (since ρ is same it will cancel out)        

• by putting the given values , cancelling common terms ,and rearrangements {DIY}..... we get the value of Y as 4Ω        

hope it will be helpful...

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