Question

If a $4\Omega$ resistance wire is doubled then calculate the new resistance of the wire.

Answer 1

Step 1: Given Data

The initial resistance on the wire $R_i=4\Omega$

Let the initial length of the wire be $L_i$.

Given that the final length of the wire $L_f=2L_i$

Let the area of the wire be $A$.

Let the resistivity of the wire be $\rho$.

Let the final resistance of the wire be $R_f$.

Step 2: Formula Used

We know that resistance is given as,

$R=\rho \frac{L}{A}$

$\Rightarrow \rho =\frac{RA}{L}$

Step 3: Calculate new Resistance

Since the resistivity of the wire is the same in both cases, we can write

$\rho =\frac{R_{i}A}{L_i}=\frac{R_{f}A}{L_f}$

$\Rightarrow \frac{R_i}{L_i}=\frac{R_f}{L_f}$

Upon substituting the values we get

$\frac{4}{L_i}=\frac{R_f}{2L_i}$

$\Rightarrow R_f=8\Omega$

Hence, the new resistance of the wire will be $8\Omega$.