If Resistance R = 10 ohms of a wire is stretched to double its length, then find new resistance.

The expression for a wire’s resistance can be illustrated as:

Here,

• ρ = Resistivity of a material
• l = Length of wire
• A = Cross-sectional area

Since length of the wire is doubled, then the cross-sectional area becomes half of its last value because volume of the given wire remains constant.

Now, the new cross-sectional area will become:

Now, the new resistance of the wire is given as: R′ = ρl′/A′

Now, after replacing the values in the formula, we can obtain:

⇒ R′ = 4ρ l/A

With further division of new resistance with last resistance, we get:

⇒ R′/R = 4

⇒ R′ = 4R

⇒ R = 10

Hence, R’ = 40Ω

Read Also: Class 12 Physics Notes

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