An electrical cable consists of 125 strands of fine wire,...

An electrical cable consists of 125 strands of fine wire, each having 2.65$\mu \Omega$ resistance. The same potential difference is applied between the ends of all the strands and results in a total current of 0.750 $\mathrm{A}$ . (a) What is the current in each strand? (b) What is the applied potential difference? (c) What is the resistance of the cable?

An electrical cable consists of 125 strands of fine wire, each having 2.65$\mu \Omega$ resistance. The same potential difference is
applied between the ends of all the strands and results in a total
current of 0.750 $\mathrm{A}$ . (a) What is the current in each strand? (b) What is the applied potential difference? (c) What is the
resistance of the cable?

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Key Concepts

Ohm's Law

Ohm's Law is a fundamental principle in electrical circuits that states the voltage across a resistor is directly proportional to the current flowing through it, represented by the formula V = IR. It is crucial for relating voltage, current, and resistance when analyzing circuits.

Parallel Circuits

Parallel circuits are arrangements where components are connected such that they share the same voltage across them. In such circuits, the total current divides among the parallel elements, and the overall resistance of the arrangement can be calculated using the reciprocal formula for resistors in parallel.

Current Division

Current division is the method by which the total current entering a parallel circuit splits among the different branches. When the resistors are identical, the current divides equally among them, making it straightforward to compute the current in each parallel element.

Equivalent Resistance Calculation

Equivalent resistance is the total or effective resistance of a network of resistors that can be reduced to a single resistor while maintaining the same voltage-current relationship as the original network. In parallel configurations, this involves taking the reciprocal of the sum of the reciprocals of the individual resistances.

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