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

Name: Problem 29, Chapter 5: Physics for IIT-JEE 2012-2013: Electricity & Magnetism
Uploaded: 2022-02-10T06:20:17-08:00
Duration: 1 min 7 s
Channel: Varsha Aggarwal
Description: An electric current is passed through a circuit containing two wires of the same material, connected in parallel. If the lengths and the radii of the wires are in the ratio of 4 / 3 and 2 / 3, then the ratio of the currents passing through the wires will be (AIEEE, 2004) a. 3 b 1 / 3 c. 8 / 9 d. 2

An electric current is passed through a circuit containing two wires of the same material, connected in parallel. If the lengths and the radii of the wires are in the ratio of $4 / 3$ and $2 / 3$, then the ratio of the currents passing through the wires will be (AIEEE, 2004) a. 3 b $1 / 3$ c. $8 / 9$ d. 2

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Key Concepts

Parallel Circuit Analysis

In a parallel circuit, each branch experiences the same potential difference, and the current through each branch is determined by its resistance. The total current is the sum of the currents through the individual branches, making it essential to analyze each branch separately when components have different resistances.

Resistance Dependence on Material and Geometry

The resistance of a conductor depends on the material's resistivity as well as its geometry—specifically, its length and cross-sectional area. Resistance increases with an increase in length and decreases with an increase in cross-sectional area, which is mathematically expressed by the formula R = ?L/A.

Impact of Cross-sectional Area (Radius) on Resistance

Since the cross-sectional area of a wire is determined by the square of its radius (A = ?r²), any change in the radius has a quadratic impact on the area, and hence the resistance, making it a critical factor when comparing conductors of different sizes in a circuit.

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