Question

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.

Answer 1

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...