Question

the resistance of the conducting wire x of length one metre is 5 whom I calculate the resistance of the wire made by the same material whose length is 4 times and the area of cross section is five times that of wire X at same temperature​

Answer 1

Correct Question

The resistance of the conducting wire X of length 1 metre is 5 ohm. Calculate the resistance of the wire made by the same material whose length is 4 times and the area of cross section is 5 times that of wire X at same temperature.

Answer

4 ohms

Explanation

We know that, resistance of wire at a constant temperature is given as

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

Here, let the area of cross section of wire X be "A" and specific resistance (resistivity) be $\sf \rho$

Then, resistance of X would be

$\sf X = \rho\frac{1}{A}$ (since, length is 1 metre)

$\sf X = \frac{\rho}{A}$

Now, a wire of same material as X has a length of 4 times and cross section 5 times as that of X at the same temperature

→ length of second wire = 4 m (4 times of 1 m is 4 m)

So, resistance of second wire would be

$\sf R = \rho\frac{4}{5A}$

We can write it as

$\sf R = \frac{4}{5} \times \frac{\rho}{A}$

We know that, $\sf\frac{\rho}{A} = X$

$\sf\implies R = \frac{4}{5}\times X$

Resistance of X given as 5 ohms

$\sf\implies R = \frac{4}{5} \times 5$

$\sf\implies R = 4\ ohm$