Question

A uniform wire of resistance $100\Omega$ its melted and made in the form of uniform wire, whose length is double that of the original. The resistance of the new wire is

• A. $200\sqrt{2}\Omega$
• B. $800\Omega$
• C. $200\Omega$
• D. $400\Omega$

Answer 1

Answer: (D)

$400\Omega$

As volume of the wire remains constant,

$Al=A^{\prime }{l}^{\prime }$

$R=\frac{\rho l}{A}$

and, $R^{\prime }=\frac{\rho l^{\prime }}{A^{\prime }}$

$\Rightarrow \frac{R^{\prime }}{R}=\frac{l^{\prime }A}{l{A}^{\prime }}$

$l^{\prime }=2l,A^{\prime }=\frac{A}{2}$

$\frac{R^{\prime }}{R}=\frac{\left(2l\right)A}{l\left(\frac{A}{2}\right)}=4$

$\Rightarrow R^{\prime }=4R$

$=4\times 100=400\Omega$