One conducting wire of length 1 m is cut into two unequal part P and Q respectively. Now, part P is stretched to double its length. Let the modified wire be R. If the resistance of the R and Q wires are same, then calculate the length of P and Q wires.
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Dear Student,
◆ Answer -
p = 20 cm
q = 80 cm
● Explanation -
# Given -
l = 1 m = 100 cm
# Solution -
Let p and q represents lengths of two segments.
When P is stretched to double its length, its cross-sectional area will be halved. Resistance of stretched wire P is -
Rp = ρ.(2p)/(A/2)
Rp = 4ρp/A
Length of wire Q will be q = 100-p. So now resistance of wire Q is -
Rq = ρ.(100-p)/A
Given that,
Rp = Rq
4ρp/A = ρ.(100-p)/A
4p = 100-p
5p = 100
p = 20 cm
Now,
q = 100-p
q = 100-20
q = 80 cm
Thus, length of P and Q is 20 cm and 80 cm respectively.
Thanks dear...
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