Question

The resistance of a wire of cross-section '$a$' and length '$l$' is $R$ $ohm$. The resistance of another wire of the same material and of the same length but cross-section '$4a$' will be

• A. $4R$
• B. $\frac{R}{4}$
• C. $\frac{R}{16}$
• D. $16R$

Answer 1

The correct option is B $\frac{R}{4}$

The electrical resistance of an electrical conductor is the opposition to the passage of an electric current through that conductor.The resistance of a wire is inversely proportional to the area of cross section of the wire. That is, the resistance of wire decreases as the diameter of the wire increases and the resistance of the wire increases as the diameter of the wire decreases.
The resistance of the conductor is given as $R=\rho \frac{l}{A}$.
In this case, the area of cross section becomes $4A$.
So, the equation becomes $R^{{}^{\prime }}=\rho \frac{l}{4A}$.
That is, $R^{{}^{\prime }}=\frac{R}{4}$.
Hence, the resistance of another wire of the same material and of the same length but cross-section '$4a$' will be $R/4$.