Question

A metallic wire of resistance $20$ ohm stretched until its length is doubled. Its resistance is

• A. $20\Omega$
• B. $40\Omega$
• C. $80\Omega$
  
• D. $60\Omega$

Answer 1

Answer: (C)

$80\Omega$

$L_1{A}_1=L_2{A}_2[\because \text{V is constant}]$

$\Rightarrow L_1\times A_1=2L_1{A}_2$

$\frac{A_1}{A_2}=\frac{2}{1}$

$\frac{R_1}{R_2}=\left(\frac{L_1}{L_2}\right)\left(\frac{A_2}{A_1}\right)$

$\frac{R_1}{R_2}=\frac{1}{2}\times \frac{1}{2}$

$\Rightarrow R_2=4\times 20$

$=80\Omega$