Question

The resistance of a $1m$ long nichrome wire is $6\Omega$. If we reduce the length of wire to $70cm,$ what will be its new resistance?

• A. $4.2\Omega$
• B. $2.4\Omega$
• C. $3.2\Omega$
• D. $6.2\Omega$

Answer 1

The correct option is A

$4.2\Omega$

Given: Resistance of $1m\left(100cm\right)$ long nichrome wire $R_1=6\Omega$
Length of nichrome wire $L_1=100cm$
Reduced length $L_2=70cm$

Let the new resistance be $R_2$.

Here, the value of $\rho$ and area of cross-section $A$ will not change.

Therefore, resistance is directly proportional to the length of the wire, so $\frac{R_1}{R_2}=\frac{L_1}{L_2}$.

On substituting the values, we get $\frac{6}{R_2}=\frac{100}{70}$

$\Rightarrow R_2=4.2\Omega$