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A square-section aluminium bar has a square hole drilled through its length, and the hole is filled with iron, forming a composite bar (the Al and Fe sections act as two parallel current paths between the end faces P and Q). Taking the resistivities of Al and Fe as 2.7 x 10⁻⁸ ohm m and 1.0 x 10⁻⁷ ohm m respectively, what is the electrical resistance measured between faces P and Q?

1. 2475/64 microohm
2. 1875/64 microohm
3. 1875/49 microohm
4. 2475/132 microohm

Correct answer: 1875/64 microohm

Solution

With the standard JEE dimensions (outer side 7 mm, inner Fe square side 2 mm, length 50 mm), the two parallel-path resistances combine to 1875/64 microohm.

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