Question

What happens to resistance when the length is doubled without steching it?

Answer 1

Step 1: Assumption
Let the new length be $2L$

Let the new resistance be $R\text{'}$
Step 2: Formula used
The formula to calculate resistance is written as:
$R=\frac{\rho L}{A}$
Where, $R$ represents the resistance, $\rho$ represents the resistivity of the material, $L$ represents the length,$A$ represents the area.
Step 3: Calculation of the new resistance
When an electric current flows through a bulb or any conductor, the conductor offers some obstruction to the current and this obstruction is known as electrical resistance
If the new length be $2L$
substitute in the resistance formula to obtain the resistance for the new length

$$\begin{gathered} R=\frac{\rho L}{A} \\ R\text{'}=\frac{\rho \left(2L\right)}{A} \\ R\text{'}=2\left(\frac{\rho L}{A}\right) \\ R\text{'}=2R \end{gathered}$$

From the above equation, we can say that as the length is doubled resistance is also doubled, if the resistivity and cross-sectional area remain the same.