a wire of resistance 2 ohm is stretched to double its length such that its volume remain constant what is the resistance of stretched wire
Answers
Explanation:
resistance of wire = 2 ohm
since the resistance of a conductor is directly proportional to the length of the conductor,
the resistance will get doubled if the length of the conductor i.e., wire is doubled
therefore the resultant resistance of the wire is
4 ohm
r=2ohm
r=rho× length/area of cross section
2=rho ×length/area of cross section ---------------- (1)
original length=l
new length =l'
from the question =2×original length =new length---------(2)
AREA OF CROSECTION×length of wire=new cross section area×new length
A×L=A'×l'
A×l=A'×(l/2)
A'=2A------------(3)
new resistance (r')=rho ×new length/new area of cross section
r'=rho×(l/2)÷2A from 2 and 3
r'=rho×l/4A
r'=1/4(rho×new length/new area of cross)
r'=1/4(2) from 1
r'=1/2
r' =0.5ohm