Question

If the length of the conductor is tripled and cross-sectional area is reduced to 50% then its resistance will be

Answer 1

Formula for resistance

$R = p\frac{l}{a}$

p = resistivity .

l = length .

a = area .

Now length of the conductor is tripled .

So the length will become 3 l .

Area is reduced by 50 %

$a=a-\frac{50}{100}\times a\\\\\implies a=a-0.5 a\\\\\implies a=0.5a$

Let us now see what will be the new resistance .

$R=p\frac{l}{a}\\\\\implies R=p\frac{3l}{0.5a}\\\\\implies R=p\frac{6l}{a}$

So the original resistance was $p\frac{l}{a}$

Ratio of the new : original will be :-

$\frac{6p\frac{l}{a}}{p\frac{l}{a}}\\\\\implies 6$

Hence the new resistance is increased to 6 times .

Answer 2

hi mate

here is your answer

pls refer to the attachment

hope it helps

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