Question

A wire of length l'and area of cross-section A was drawn into a wire of
double its length by melting it. If its original resistivity and resistance were
p and R respectively, what will be its new resistivity and resistance ?​

Answer 1

Answer:

After melting the length of the wire would become double and area of cross-section would be halved.

i. e. Length of wire l'=2l

Area of cross-section A' =A/2

R= p l/A

R' = pl'A'

R'=p 2l/(A/2)=4(pl/A)

R'=4R

Therefore the new resistance of the wire is 4R.

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Answer 2

Answer:New Resistance = 4×Old Resistance

             New Resistivity=Old Resistivity

Explanation:

Before melting

length= l'              area of cross section=A

Volume=l'×A

Resistance,R=pl'/A

Resistivity,p=RA/l'

After Melting

Length=L1           Area of cross section=A1

Given that L1=2l'

Volume=L1×A1=2l'×A1

Volume will remain Constant

Volume before melting = Volume after melting

l'×A=2l'×A1

A=2A1

New Resistance=R'=p'L1/A1

Put L1=2l'  A1=A/2

R'=4pl'/A

R'=4R

New Resistivity=p'=R'A1/L1

Put R'=4R        A1=A/2       L1=2l'

p'=RA/l'

p'=p