You are given a wire of length 100 cm and linear resistance of 1 ohm/cm.if it is cut into two parts,so that when they are in parallel, the effective resistance is 24 ohmthe lengths of the two parts are

Soumya Ranjan Mohanty
117 Points
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) = x(100-x)/(x+100-x). But in question it is given to be 24. So they must be equal. Equating, we get x(100-x)/100=24 =>100x-x^2=2400=>x^2-100x+2400=0 =>x^2-40x-60x-2400=0 =>x(x-40)-60(x-40)=0 => x=40 cm or x=60 cm.
When, x=40 cm, the other part is 100-x=60 cm.
When x=60 cm , the other part is 100-x=40 cm.
So, the lengths of the 2 parts were 40 cm and 60 cm.
Thanks.
Vikas TU
14149 Points
7 years ago
Dear Student,

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

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