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*(2l)/((A)/(2)) \\ \\ R_2=\rho*(2*2l)/(A) \\ \\ R_2=4\rho(l)/(A) \\ \\ R_2=4R \end{gathered}`

Where:

R2 is the new reistance.

Thus, we have:

`\begin{gathered} R_2=4R \\ \\ R_2=4*100=400\Omega \end{gathered}`

Therefore, the new resistance is 400 ohms.

ANSWER:

`400\text{ }\Omega`