(a) Find the equivalent resistance between points A and B...

(a) Find the equivalent resistance between points $A$ and $B$ for the combination of resistors shown. (b) What is the potential difference across each of the $4.0-\Omega$ resistors? (c) What is the current in the $3.0-\Omega$ resistor?
(FIGURE CAN'T COPY)

Key Concepts

Current Division

The current division principle applies to parallel circuits and describes how the total current entering a junction splits among the parallel branches. The current in each branch is inversely proportional to the branch’s resistance, allowing the calculation of the current through any specific resistor in the parallel network.

Equivalent Resistance

Equivalent resistance is the total resistance that a circuit presents to an external source when multiple resistors are combined. By reducing a network of resistors into a single resistor using series and parallel combinations, it simplifies calculations of circuit behavior such as current flow and voltage distribution.

Series Resistor Combination

In a series resistor combination, resistors are arranged end-to-end so that the same current flows sequentially through each. The total resistance is simply the sum of the individual resistances. This configuration causes the applied voltage to be divided among the resistors proportionally to their resistances.

Parallel Resistor Combination

In a parallel resistor combination, resistors are connected across the same two points so that the voltage across each resistor is identical. Instead of adding directly, the reciprocals of the resistances are summed to find the reciprocal of the equivalent resistance, which results in a lower total resistance than any individual resistor in the parallel network.

Ohm's Law

Ohm's Law is a fundamental relation in circuit analysis which states that the voltage (V) across a resistor is directly proportional to the current (I) flowing through it and the resistance (R) of the resistor, expressed as V = IR. This principle is essential for analyzing and solving electrical circuits.

Voltage Division

The voltage division principle explains how the total voltage in a series circuit is divided among the resistors based on their resistance values. Each resistor in series drops a portion of the total voltage proportional to its resistance, making it straightforward to calculate the voltage across any individual resistor in the chain.

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