A wire of uniform cross section and length l

Asked by admin @ 20/08/2021 in Physics viewed by 344 People

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.

Answered by admin @ 20/08/2021

Question:

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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