An electric current is passed through a circuit containing...

An electric current is passed through a circuit containing two wires of the same material, connected in parallel. If the lengths and radii of the wires are in the ratio of $4 / 3$ and $2 / 3$, then the ratio of the currents passing through the wire will be (A) 3 (B) $1 / 3$ (C) $\underline{8 / 9}$ (D) 2

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Key Concepts

Electrical Resistance

Electrical resistance is a fundamental concept that quantifies how much a material opposes the flow of electric current. The resistance of a conductor is determined by its resistivity, a material property, as well as its geometrical dimensions. It is given by the formula R = (?L)/(A), where ? is the resistivity, L is the length, and A is the cross-sectional area.

Dependence of Resistance on Geometric Dimensions

The resistance of a conductor is directly proportional to its length and inversely proportional to its cross-sectional area. Since the cross-sectional area of a wire is given by A = ?r², the resistance decreases as the radius increases, and increases as the length increases. This relationship is pivotal when comparing conductors of the same material but different dimensions.

Current Division in Parallel Circuits

In a parallel circuit, all branches experience the same voltage. According to Ohm’s law, the current through a branch is inversely proportional to its resistance. This means that a branch with a lower resistance will carry a greater portion of the total current, while a branch with a higher resistance will carry less. This principle is essential in analyzing how electric current divides among different paths in a parallel circuit.

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