Question

A particular resistance wire has a resistance of 3.0 ohm per metre. The resistance of 5 m length of a wire of the same material, but with twice the area of cross section will be :

• A. $2.5\Omega$
• B. $5\Omega$
• C. $3\Omega$
• D. $7.5\Omega$

Answer 1

The correct option is D $7.5\Omega$

In the question, it is given that the resistance of one meter wire is 3 ohms. So the resistance of 1.5 meters of the same wire is given as $\frac{3\times 5}{1}=15ohms$.

The resistance of a resistor is given by the formula $R=\rho \frac{L}{A}$ where $\rho$ is the resistivity of the material the resistor is made of, l is the length of the resistor and A is the cross-sectional area.

Let the resistance of the wire is initially equal to R. $R=\rho \frac{L}{A}$ .

When the area of cross-section of the wire is doubled and so the resistance of the wire is given as $R^{{}^{\prime }}=\rho \frac{L}{2\left(A\right)}$.

The new resistance is $R^{{}^{\prime }}=\frac{R}{2}$.

Hence, the changed resistance of the wire is 15/2=7.5 ohms.