Question

Two wires A and B are madeup of two different materials and have equal thickness and equal resistances.Whichwireislonger?Justify Your answer.Given resistivity of material of wire B is greater than that of A​

Answer 1

Since resistance of wire A and wire B is same, we can say:

$R_{A} = R_{B}$

$\implies \dfrac{ \rho_{A} \times l_{A}}{area_{A}} = \dfrac{ \rho_{B} \times l_{B}}{area_{B}}$

• Now, Thickness is same for both wires. So, area is equal.

$\implies \rho_{A} \times l_{A} = \rho_{B} \times l_{B}$

$\implies \dfrac{ l_{A} }{l_{B}}= \dfrac{\rho_{B}}{ \rho_{A}}$

• Now, resistivity of B > A, so we will say:

$\implies \dfrac{ l_{A} }{l_{B}} > 1$

$\implies l_{A} > l_{B}$

So, wire A is longer than wire B .