A metal wire of resistance R is cut into two pieces of equal...

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Key Concepts

Resistors in Parallel

When two or more resistors are connected in parallel, the overall or equivalent resistance decreases because the current can split among the different branches. The equivalent resistance is calculated by taking the reciprocal of the sum of the reciprocals of the individual resistances, which for two identical resistors results in an effective resistance that is half of one resistor's value.

Electrical Resistance

Electrical resistance quantifies how a material opposes the flow of electric current and is influenced by the material's properties, its length, and its cross-sectional area. In uniform materials, longer wires typically have higher resistance, while thicker wires have lower resistance.

Geometric Scaling of Resistance

The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area. When a wire is cut into equal lengths, each segment’s resistance is reduced in proportion to its shortened length, assuming the material and cross-section remain constant.

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