Question

A resistance of 2 ohm is to be made from a copper wire ( specific resistance 1.7×10^-8 ohm meter using a wire of length 50cm. The radius of wire is

Answer 1

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Answer 2

Answer:

The radius of wire is $r=3.6\times 10^{-5}\ m$

Explanation:

It is given that,

Resistance of the copper wire, R = 2 ohm

Specific resistance of the wire, $\rho=1.7\times 10^{-8}\ \Omega-m$

Length of the wire, l = 50 cm = 0.5 m

We need to find the radius of the wire. The resistance of the wire is given by:

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

$R=\rho\dfrac{l}{\pi r^2}$

Where

r is the radius of the wire

$r^2=\dfrac{\rho l}{R\pi}$

$r^2=\dfrac{1.7\times 10^{-8}\times 0.5\ m}{2\times \pi}$

$r=\sqrt{1.35\times 10^{-9}}$

r = 0.000036 meters

$r=3.6\times 10^{-5}\ m$

So, the radius of the wire is $3.6\times 10^{-5}\ m$. Hence, this is the required solution.