A wire is bent in the form of a circle of radius 4 m Resistance per unit length of wire is 1 /

step 1 In this question, a wire band in the form of a circle of radius, 4 meter, radius is given r is e

A wire is bent in the form of a circle of radius 4 m...

A wire is bent in the form of a circle of radius $4 \mathrm{~m}$ Resistance per unit length of wire is $1 / \pi \Omega / \mathrm{m}$ battery of $6 \mathrm{~V}$ is connected between $\mathrm{A}$ and $\mathrm{B} \angle \mathrm{AOB}=90^{\circ}$ Find the current through the battery (A) $8 \mathrm{~A}$ (B) $4 \mathrm{~A}$ (C) $3 \mathrm{~A}$ (D) $9 \mathrm{~A}$

A wire is bent in the form of a circle of radius $4 \mathrm{~m}$ Resistance per unit length of wire is $1 / \pi \Omega / \mathrm{m}$ battery of $6 \mathrm{~V}$ is connected between $\mathrm{A}$ and $\mathrm{B} \angle \mathrm{AOB}=90^{\circ}$ Find the current through the battery
(A) $8 \mathrm{~A}$
(B) $4 \mathrm{~A}$
(C) $3 \mathrm{~A}$
(D) $9 \mathrm{~A}$

Key Concepts

Parallel Resistors and Equivalent Resistance

In circuit analysis, when current has multiple paths to follow between two nodes, the resistances in these parallel branches combine to give an equivalent resistance that is lower than any individual branch resistance. The formula for combining parallel resistors is key to determining the net effect of multiple resistive paths on current distribution.

Division of a Continuous Resistor into Segments

When a continuous resistor, such as a wire, is bent into a specific shape, it is often useful to conceptually divide it into segments to analyze different parts of the circuit. Each segment’s resistance can be determined based on its length relative to the total length of the conductor, allowing for circuit simplification and the application of series or parallel resistance formulas.

Application of Geometry in Circuit Analysis

The geometry of a circuit, such as the division of a circular wire into arcs, plays an important role in determining the individual resistances of different segments. By relating angles or arc lengths to the total circumference, one can calculate the resistance of each segment, which in turn aids in forming the appropriate equivalent circuit for analysis.

Ohm's Law

Ohm's Law is a fundamental principle in electrical circuits that states the current through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance between them. This relationship, expressed as V = IR, is crucial for analyzing how applied voltages drive currents through various circuit components.

Resistance per Unit Length

Resistance per unit length is a characterization of materials or conductors in which the resistance is uniformly distributed along its length. It allows one to calculate the resistance of any segment of the conductor by multiplying the total length of that segment by the given resistivity value, thus enabling precise modeling of continuous resistive objects.

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