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You are given a wire of length 100100 cm and linear resistance of 11 ohm/cmohm/cm.if it is cut into two parts,so that when they are in parallel, the effective resistance is 2424 ohmthe lengths of the two parts are

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Srihari , 7 Years ago
Grade 12th pass
anser 2 Answers
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Soumya Ranjan Mohanty

Last Activity: 7 Years ago

let length of one part of wire= x cm, so other part’s length =100-x cm. Given that linear resistance is 1 ohm/cm i.e 1 cm has 1 ohm resistance. So x cm has x * 1=x ohm resitance and 100-x cm has 100-x*1 ohm=100-x ohm resistance. The parallel combination of these 2 parts of wires will give effective resistance as R1R2/R1+R2 = x100-x/x+100-x. But in question it is given to be 24. So they must be equal. Equating, we get x100-x/100=24 =>100x-x^2=2400=>x^2-100x+2400=0 =>x^2-40x-60x-2400=0 =>xx-40-60x-40=0 => x=40 cm or x=60 cm.
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When, x=40 cm, the other part is 100-x=60 cm.
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When x=60 cm , the other part is 100-x=40 cm.
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So, the lengths of the 2 parts were 40 cm and 60 cm.
rn
Thanks.

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Vikas TU

Last Activity: 7 Years ago

Dear Student,

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One part is x and the other one is 100-x
linear resistance=L=1W/cm
ATQ
1/Lx + 1/L100-x = 1/24
=>1/x+1/100-x = 1/24
=>100/x100-x = 1/24
=>x2-100x+2400=0
=>x=150 or -50
Neither can be the answer. Hence the data is wrong.rn
Cheers!!

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Regards,
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Vikas B. Tech. 4th year
Thapar University
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