The resistance of a wire is r - The wire is stretched to double its length- then its resistance is

The correct option is B 4r Given resistance of wire = r Ω r = ρL_1/A_1 When the wire is stretched to double its length, the radius will decrease as such the v ...

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Standard X

Physics

Factors Affecting Resistance & How They Affect

The resistanc...

Question

The resistance of a wire is r $Ω$ . The wire is stretched to double its length, then its resistance is

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Solution

The correct option is B
4r

Given resistance of wire = r $Ω$

r = $\frac{ρ L_{1}}{A_{1}}$

When the wire is stretched to double its length, the radius will decrease as such the volume remains constant.

$A_{1}$ $L_{1}$ = $A_{2}$ $L_{2}$

$A_{1}$ $L_{1}$ = $A_{2}$ $\times 2 L_{1}$

$A_{2}$ = $\frac{A_{1}}{2}$

Now, r' = $\frac{ρ L_{2}}{A_{2}}$ = $\frac{ρ \times 2 L_{1}}{\frac{A_{1}}{2}}$ = $\frac{4 ρ L_{1}}{A_{1}}$ = 4r

Suggest Corrections

The resistance of a wire is r Ω. The wire is stretched to double its length, then its resistance is

The correct option is B 4r Given resistance of wire = r Ω r = ρL1A1 When the wire is stretched to double its length, the radius will decrease as such the volume remains constant. A1L1 = A2L2 A1L1 = A2×2L1 A2 = A12 Now, r' = ρL2A2 = ρ×2L1A12 = 4ρL1A1 = 4r

The resistance of a wire is r $Ω$ . The wire is stretched to double its length, then its resistance is