Question

A wire of uniform cross-section and length l has a resistance of 4 . The wire is cut into four equal pieces. Each piece is then stretched to length l'. Thereafter, the four wires are joined in parallel. Calculate the net resistance.

Answer 1

Question:

A wire of uniform cross-section and length l has a resistance of 4 . The wire is cut into four equal pieces. Each piece is then stretched to length l'. Thereafter, the four wires are joined in parallel. Calculate the net resistance.

Answer:

Length of wire = L

resistance of wire = 16 Ohm = R ( Let)

now, wire cut four equal parts

e.g Length of each part = L/4

we know,

R = ρL/A

where ρ is resistivity ( constant )

when we cut the wire , cross section area won't be change .

hence, R is directly proportional to L

so, each part have resistance = R/4

again,

According to question ,

each part stretched and length increases L/4 to L

[ when , we stretched the wire , volume of wire is constant ]

R = ρL²/AL

AL = volume of each wire ( constant)

hence, R is directly proportional to L²

L is increased to four times so,

R' = 16( R/4) = 4R

hence, each of wire have 4× 16 = 64 ohm resistance .

now,

all wire connected in parallel .

e.g 1/R₁ + 1/R₂ + 1/R₃ + 1/R₄ = 1/Req

1/Req = 1/64 + 1/64 + 1/64 + 1/64

1/Req = 4/64

1/Req = 1/16

Req = 16 ohm

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Answer 2

Answer:-

• resistance = 4 ohm

wire is cut into 4 equal parts therefore,

net resistance =1/R =1/R1 +1/R2 + 1/R3 + 1/R4

= 1/4 +1/4 +1/4 +1/4

= 4/4=1

1/R= 1

R =1