Question

A 100 Ω wire resistor has its length doubled. What is its new resistance?

Answer 1

Given the resistance of a wire:

R = 100 Ω

If the length of the wire is doubled, let's find the new resistance.

When the length of a wire is increased to double the original length, the cross sectional area of the reduces by half.

Thus, we have the formula:

$\begin{gathered} R_2=\rho\times\frac{2l}{\frac{A}{2}} \\ \\ R_2=\rho\times\frac{2\times2l}{A} \\ \\ R_2=4\rho\frac{l}{A} \\ \\ R_2=4R \end{gathered}$

Where:

R2 is the new reistance.

Thus, we have:

$\begin{gathered} R_2=4R \\ \\ R_2=4\times100=400\Omega \end{gathered}$

Therefore, the new resistance is 400 ohms.

ANSWER:

$400\text{ }\Omega$