Question

The resistance of a conducting wire X of length 1 m is 50. Calculate the
resistance of the wire made by the same material whose length is 4 times
and area of erone section is 5 times that of whre x (At some temperature),​

Answer 1

Correct Question

The resistance of a conducting wire X of length 1 m is 50. Calculate the resistance of the wire made by the same material whose length is 4 times and area of cross section is 5 times that of wire X (At same temperature).

Answer

40 ohms

$\sf\rule{200}2$

Explanation

Experimentally, it is found that resistance of a current carrying conductor is directly proportional to its length and inversely to its area of cross section. This gives

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

Where, $\sf\rho$ is the constant of proportionality and its called as the resistivity or specific resistance of the conductor.

For same material, resistivity is same.

For wire X, let area of cross section be A and resistivity be $\sf\rho$. Thus, we get

$\sf 50 = \rho\frac{1}{A}$

$\sf 50 = \frac{\rho}{A}$ ..............(1)

Now, another wire of same material has length 4 times that of X, so length of another wire = 4 m (4 × 1 m = 4 m)

And, area of cross section is 5 times that of wire X

→ area of cross section = 5A

So, resistance of another wire would be

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

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

From (1), we get

$\sf R = \frac{4}{5} \times 50$

$\sf R = 40$

Hence, resistance of second wire is 40 ohm.

Answer 2

Answer:

Explanation:

→ Initial resistance for wire X = 5 ohm = p(L/A)

→ Now, length of new wire = 4 times

→ Area of new wire = 5 times

→ Hence , new resistance be R"

→ R" = p(L"/A")

→ R" = p(4L/5A)

→ R" = p(L/A) × 4/5

→ R" = 5 × 4/5

→ R" = 4 ohms.

→ so resistance = 4 ohm