Question

A wire of resistance 12 ohm is stretched so that its length is doubled and the area of cross section is halved. How will its resistance change?

Answer 1

➶➶➶➶➶[ ANSWER ]➷➷➷➷➷

◼Resistance of a wire is directly proportional to length, so of length would have been increased the resistance will also be increased.

◼The resistance of wire is inversely proportional to area of cross section so, if the resistance will be decreased too.

so, calculated the new resistance

Let Original length =2 l.

and let area of cross section =a.

so, resistance be

R=a/l.

12 =a/2l.

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◼Given,

area of sector is halved so,

new area of cross section a1=a/2.

and length is doubled so,

new length l1=l

New resistance R1 =a1/l1

R1=a/2÷l

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◼Now, On dividing original resistance with the new resistance...

R1/R=a1/l1÷a/l..

R1/12=a/2/l ÷a/2l

so, after calculation it comes that the resistance becames 4times of original resistance means..

12×4=48 ohms.

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ஜ۩۞۩ஜ[ Hope it helps ]ஜ۩۞۩ஜ

Answer 2

We know that R = p l/a

If length is doubled and area of cross section is halved, the new resistance is R' p 2l/a/2 = 4(p L /a) = 4 R

= 4 ×12 = 48 ohm