Question

By how many times does doubling the diameter of a wire and making it 10 times longer increase its resistance
a)2.5 times
b)5 times
c)10 times
d)30 times
plz solve this

Answer 1

Question :-

By how many times does doubling the diameter of a wire and making it 10 times longer increase its resistance  

a) 2.5 times  

b) 5 times  

c) 10 times  

d) 30 times

Answer starts

By relation :

R = p l / a

For a wire :

R = p l / π r²

where r is the radius

Let d be the diameter .

d = 2 r

r = d/2

r² = d²/4

= > R = p l / ( π d² / 4 )

Observations from the relation :

If diameter is doubled , then resistance will decrease to one-fourth.

This is because Resistance is inversely proportional to square of diameter.

If length is increased by 10 times then the resistance also increases 10 times as length is directly proportional to resistance .

Thus new resistance will increase 10 times as well as decrease to one fourth .

So over all it increases 10/4 times

                                    = 2.5 times

ANSWER :-

OPTION A

Answer 2

Explanation:

option A is the correct answer