Question

A wire of resistance $10\Omega$ is cut into 4 equal parts, keeping it's area the same, what will be the new resistance of each part?

• A. $1.5\Omega$
• B. $3.5\Omega$
• C. $2.0\Omega$
• D. $2.5\Omega$

Answer 1

The correct option is D $2.5\Omega$

When the area of two wires are same then the resistance of the wire is directly proportional to the length of the wire:
$\frac{R_1}{R_2}=\frac{l_1}{l_2}\Rightarrow \frac{10}{R_2}=\frac{l}{\frac{l}{4}}\Rightarrow \frac{4l}{l}$
$R_2=\frac{10}{4}=2.5\Omega$
$R_2=2.5\Omega$