A strand of wire has resistance 5.60 μΩ. Find the net resistance of 120 such strands if they are

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A strand of wire has resistance 5.60 μΩ. Find the net...

A strand of wire has resistance 5.60 $\mu \Omega$. Find the net resistance of 120 such strands if they are (a) placed side by side to form a cable of the same length as a single strand, and (b) connected end to end to form a wire 120 times as long as a single strand.

Key Concepts

Dependence of Resistance on Wire Geometry

The resistance of a conductor is affected by its geometry based on the relation R = ?L/A, where R is resistance, ? is resistivity, L is the length, and A is the cross-sectional area. Altering the length or the area—such as by connecting wires in series (changing L) or in parallel (changing A)—directly influences the total resistance. This concept underpins the transition between series and parallel configurations.

Series Connection of Resistive Elements

In a series arrangement, resistors (or wire segments) are connected end-to-end so that the same current flows sequentially through each element. The total resistance is simply the sum of the individual resistances. This concept is fundamental when considering how increasing the length of a conductor (by connecting wires in series) increases overall resistance.

Parallel Connection of Resistive Elements

In a parallel arrangement, multiple resistors or conductive strands are connected across the same two points, providing several paths for the current. The overall resistance is determined by the reciprocal of the sum of reciprocals of the individual resistances, resulting in a total resistance lower than any individual resistor. This principle is used when strands are placed side-by-side, effectively increasing the cross-sectional area and reducing resistance.

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