Question

The resistance of a conducting wire X of length 1 m is 5ohm. Calculate the resistance of the wire made with the same material whose length is 4 times and area of cross section is 5 times that of wire X ( At same temperature )​

Answer 1

Answer:

4ohm

Explanation:

length is directly proportional and cross sectional area is inversely proportional

Answer 2

The resistance of wire X is 4 ohm .

We know , resistance of a material is given by :

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

Here , $\rho$ is specific resistance of the material .

L is length of the resistor.

A is area of the resistor.

In the given question resistance is 5 ohm .

$5=\dfrac{\rho L}{A}$

Now, when length is 4 times and area is 5 times .

Let , the new resistance is x .

$x=\dfrac{\rho 4L}{5A}=\dfrac{4}{5}\dfrac{\rho L}{A}=\dfrac{4}{5}\times 5=4\ ohm.$ { putting value of $\dfrac{\rho L}{A}=5\ ohm$ in above equation }

The resistance of wire X is 4 ohm .

Hence , this is the required solution.

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