Question

Figure (a), (b) and (c) show three cylindrical copper conductors along with their face areas and length. Which of the conductors will have highest resistance and why?

Answer 1

Considering all the three cylinders one by one and substituting the values in the formula,

(1) For the cylinder in case (a),

\(R = \rho \frac LA\)

(2) For the cylinder in case (b),

\(R = \rho \frac{2L}{A/2} = 4\rho \frac LA\)

(3) For the cylinder in case (c), the resistance is,

\(R = \rho \frac {L/2}{2A} = \rho \frac L{4A}\)

As we compare the three cases, we come to know that the resistance of the cylinder in (b) is maximum as it has twice the length and half the area.

Answer 2

Hence, R_b >R_a > R_c. Thus, the conductor (b) will have the highest resistance.