A wire of cross-sectional area 5.0× $1 0^{- 6}$ $m^{2}$ is made of a metal of resistivity 50× $1 0^{- 8}$ Ωm. The potential difference across the wire is 6.0V and the current is 3.0A. What is the length of the wire?

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0.050m

0.20m

5.0m

20m

answer is D.

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Detailed Solution

Concept: All materials have a characteristic called resistivity that determines whether they are insulators or conductors. It is described as the resistance provided by a conductor with a 1 m length and a 1 m2 cross-section.
Any substance that tries to oppose the flow of electric current has a property known as electrical resistance. It mostly depends on resistivity, a feature that all materials have by nature. The resistivity of any substance tells whether or not it is a conductor.
insulator. A substance is an insulator if it has an extremely high resistance. However, if it has a low resistance, the substance is a conductor. The ohm-metre(m) is its SI unit. Resistivity may be used to compute electrical resistance by,

R = \frac{ρl}{A} .

. . . . . . . (1)
Where, R=Electrical resistance of the conductor, ρ=Resistivity of the conductor,

l =

Length of the conductor and A=Cross-sectional Area of the conductor.
Now, according to Ohm’s Law, the potential difference across any conductor is directly proportional to the electrical current flowing through the conductor. That is,