A 40-volt power supply is connected across points A and B of...

A 40-volt power supply is connected across points A and B of Figure 10-4. The current through one of the 10 -ohm resistors is_________
(a) 1.6 amperes
(b) 2 amperes
(c) 4 amperes
(d) 8 amperes
(e) 16 amperes.

Key Concepts

Ohm's Law

Ohm's Law defines the fundamental relationship between voltage, current, and resistance in an electrical circuit. It states that the current through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance, represented mathematically as I = V/R. This principle is essential for analyzing and solving circuit problems, including the determination of currents in resistor networks.

Series and Parallel Resistors

Understanding series and parallel resistor configurations is crucial in circuit analysis. In a series circuit, resistors are connected end-to-end, and the total resistance is the sum of the individual resistances. In a parallel circuit, resistors are connected across the same two nodes, and the reciprocal of the total resistance is the sum of the reciprocals of the individual resistances. Determining the equivalent resistance through which the power supply voltage is applied simplifies the analysis of the overall circuit.

Equivalent Resistance

Equivalent resistance is a concept used to simplify complex resistor networks into a single resistor that has the same effect on the circuit as the original network. By converting series and parallel groups of resistors into a single equivalent resistor, it becomes easier to apply Ohm's Law and other circuit analysis techniques to determine currents and voltages within the circuit.

Current Division Rule

The current division rule is a technique used to determine the distribution of current among parallel branches in a circuit. It states that the current through any branch is inversely proportional to its resistance relative to the total parallel resistance. This rule is essential when analyzing circuits where a known total current or voltage must be divided among several resistive paths.

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