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Question

# The resistance of a wire is 24 ohm. What will be the new resistance if (a) only the length of the conductor is increased to 3 times of its original length. (b) only the cross section area of the wire is doubled?

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Solution

## Step 1: Given that:The resistance(R) of the wire= 24ΩStep 2: a) Calculation of new resistance when only the length is increased to 3 times:Let the original length of the wire is l , thenWe know that;Resistance of a conductor ∝ the length of the conductor.Thus,If only the length of the conductor is increased by 3 times, its resistance will also be increased by 3 times.Therefore the new resistance = 3R = 3×24Ω = 72Ω Step 3: Calculation of new resistance when only the area of cross-section is doubled:The resistance of a conductor is inversely proportional to the area of cross-section of the conductor.That is;R∝1A Thus,As the area of the cross-section is doubled, the resistance of the conductor will be halved.Thus,New resistance= 24Ω2=12Ω Thus,The new resistance when only length is incresed= 72Ω when only area of cross-section is increased= 12Ω

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