Question

The resistance of a wire of 0.01 cm radius is lor.
If the resistivity of the material of the wire is 50x10 ohm
meter, find the length of the wire?
T
oinette​

Answer 1

Correct Question:

The resistance of a wire of 0.01 cm radius is 10 ohm. If the resistivity of the material of the wire is $\sf{5.03\times 10^{-8}}$ ohm meter, find the length of the wire.

Solution:

Given:

=> R = 10 Ω

=> r = 0.01 cm = $\sf{10^{-4}\;m}$

=> ρ = $\sf{5.03\times 10^{-8}\Omega\;m}$

To Find:

=> Length of wire

Formula used:

$\sf{\implies R = \rho \dfrac{l}{A}}$

So,

$\sf{\implies Area\;of\;wire = \pi r^{2}}$

$\sf{\implies 3.14\times 10^{-8} \;m^{2}}$

So,

$\sf{\implies R = \rho \dfrac{l}{A}}$

$\sf{\implies l = \dfrac{R\times A}{\rho}}$

$\sf{\implies \dfrac{10\times 3.14\times 10^{-8}}{5.03\times 10^{-8}}}$

$\large{\boxed{\boxed{\sf{\blue{\implies l = 6.24\;m}}}}}$

Answer 2

Given :-

Radius (R) = 10 ohm.

Resistance (r) = 0.01 cm = 10^4 m.

resitvity (p) = 5.03 × 10^ -8 ohm m.

To Find :- Length of the wire.

Solution :-

We know R = p l/A

Where l stands for length and A stands for area.

l = RA/ p

Substituting the value,

Area = π(r)^2

l = 10 × 3.14 (10^4)^2 / 5. 03 × 10^-8

l = 31.4 (10^4)^2 / 5.03 × 10^-8

l = 6.24 m

Therefore, the length of wire is 6. 24 m.