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JEE Main 2022 (30 Jun, Shift 1) · Combination of Resistors

Combination of Resistors question from JEE Main 2022 (30 Jun, Shift 1)

Q40JEE Main 2022 · 30 JUN · SHIFT 1Medium

Combination of Resistors

An electric cable of copper has just one wire of radius 9 mm. Its resistance is 14 $\Omega$ . If this single copper wire of the cable is replaced by seven identical well insulated copper wires each of radius 3 mm connected in parallel, then the new resistance of the combination will be:

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Answer: (b)

Same length, $R \propto \dfrac{1}{r^2}$ .
One wire of radius 3 mm: $R' = 14 \times \left(\dfrac{9}{3}\right)^2 = 126\ \Omega$ .
Seven in parallel: $\dfrac{126}{7} = 18\ \Omega$
So the answer is (b) $18\ \Omega$ .

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