Question

The resistance $R$ in terms of length $L$ and cross section $A$ and resistivity $\rho$ of wire is given by

• A. $\frac{\rho L}{A^2}$
• B. $\frac{\rho L}{A}$
• C. $\frac{\rho L^2}{A^2}$
• D. $\frac{\rho L^2}{A}$

Answer 1

Answer: (B)

$\frac{\rho L}{A}$

The total amount of resistance to charge flow within a wire of an electric circuit is affected by some clearly identifiable variables.

• The total length of the wires will affect the amount of resistance. The longer the wire, the more resistance that there will be. There is a direct relationship between the amount of resistance encountered by charge and the length of wire it must traverse. If resistance occurs as the result of collisions between charge carriers and the atoms of the wire, then there is likely to be more collisions in a longer wire. More collisions mean more resistance.
• The cross-sectional area of the wires will affect the amount of resistance. Wider wires have a greater cross-sectional area. The wider the wire, the less resistance that there will be to the flow of electric charge. When all other variables are the same, charge will flow at higher rates through wider wires with greater cross-sectional areas than through thinner wires.
• Another factor that affects the resistance to charge flow is the material that a wire is made of. Not all materials are created equal in terms of their conductive ability. Some materials are better conductors than others and offer less resistance to the flow of charge. Silver is one of the best conductors but is never used in wires of household circuits due to its cost. Copper and aluminum are among the least expensive materials with suitable conducting ability to permit their use in wires of household circuits.
• Hence correct option is C.