Chapter 18, Problem 1OQ

To determine

The conductor with the least resistance.

Answer to Problem 1OQ

Solution: The conductor (b) gives the greatest resistance while the conductor (c) gives the least resistance.

Explanation of Solution

The resistance of a cylindrical conductor is given by:

R = $R=\rho \frac{l}{A}$ , where ρ is resistivity, l is the length and A is the cross-sectional area.

As we can see, resistance is directly proportional to length and inversely proportional to area (or diameter).

Among the four conductors given, (b) has the greatest length and the least diameter, so it would have the greatest resistance.

Conductor (c) has the least length and the greatest diameter, so it would offer the least resistance.

Conclusion: Thus, the required answer is determined.