Question

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Answer 1

QUESTION :

A wire of length L and resistance R is stretched so that its length is doubled. How will the

a) Resistance change

b) Resistivity change ?

SOLUTION :

Since, Resistivity do not depend on the Length or area of cross section of any conductor therefore, On stretching the wire there will not be any change in the Resistivity of Wire. so the resistivity will remain constant.

Let, the constant resistivity of wire = ρ

According to question,

• Initial Length of wire = L
• Initial area of cross section of Wire = A
• Initial Resistance of Wire = R

When wire is stretched to double its length then,

• New Length of wire = 2 L
• New area of cross section of wire = A / 2
• Let, new resistance of wire = R'

Using relation

• R = ρ L / A

[ where R is the resistance, ρ is resistivity, L is length and A is area of cross section of Conductor ]

Initial resistance of wire will be

→ R = ρ L / A  _____ equation (1)

New resistance of wire will be

→ R' = ρ ( 2 L ) / ( A / 2 )

→ R' = ( 2 ρ L ) × ( 2 / A )

→ R' = 4 ( ρ L / A )

Using equation (1)

→ R' = 4 R

therefore,

• New Resistance of wire will be 4 times of the Initial resistance.