Question

A wire of resistance $100$ $\Omega$ is doubled on itself. The new resistance is

• A. $100$ ohms
• B. $200$ ohms
• C. $300$ ohms
• D. $400$ ohms

Answer 1

The correct option is D $400$ ohms

Let, the resistance of the resistor is R, length of resistor is L and cross-sectional area is A.

We know, $R\propto L$ and $R\propto \frac{1}{A}$

Also, when the length of resistor is doubled its cross-section area is halved therefore due to combined effect of these two R will decrease.

Hence, the new resistance say $R_n$ is

$R_n=\left(4\right)R$

$R_n=\left(4\right)\times 100$

$R_n=400\Omega$