Resistance of a wire is r ohms. The wire is stretched to double its length, then its resistance in ohms isa)r / 2b)4 rc)2 rd)r / 4.Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Resistance ‘R = 6ohm’ is related to length ‘L’, area of cross-section ‘A’ and resistivity ‘ρ’ as,

R = ρL/A

When L is doubled ,

As we know that the volume of the wire remains same.

old volume = new volume

AL = A'L' ....(i) ( as volume = area x length )

L' = 2L

So, from (i)

A' = A/2

So the new resistance is ,

R' = ρL'/A'

or

R' = ρ(2L)/(A/2) = 4 (ρL/A)

=> R' = 4R

thus, correct answer is option (b).

Answer

Answer

Explanation:

When a wire is stretched to double its length, its cross-sectional area is reduced by half. This means that the new resistance can be calculated using the formula:

R' = (ρL')/A'

where R' is the new resistance, ρ is the resistivity of the material (a constant), L' is the new length, and A' is the new cross-sectional area.

Let's assume that the original resistance of the wire is R. Therefore, its original length is L and its original cross-sectional area is A.

Now, when the wire is stretched to double its length:

New length, L' = 2L
New cross-sectional area, A' = A/2 (since the wire is stretched, its cross-sectional area is reduced by half)

Substituting these values in the formula, we get:

R' = (ρ(2L))/(A/2)
R' = 4ρL/A
R' = 4R (since R = ρL/A)

Therefore, the new resistance of the wire is four times the original resistance. In other words, the resistance is doubled when the length of the wire is doubled.

Hence, the correct option is B) 4R.

Answer

We know that, resistance is directly proportional to the length of wire so answer is 2r

Answer

R=Pl/A (r=Pl/A. ) 1 now length get doubled=2L therefore,area get halved=A/2 new resistance (R')=2PL/A)2 R'=4PL/A R'=4r(B)

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