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Question
How will the resistance of a wire be affected if its
- length is doubled, and
- radius is also doubled ?
Give justification for your answer.
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Solution
R `=(rho"l")/"A"`
Where, `rho` = electrical resistivity
l = length of the conductor
A = cross-sectional area of the conductor
Hence if the length is double then
⇒ `"R"_1=rho((2"l"))/"A"`
`therefore "R"_1 = 2("R")`
So, if the length of the resistance gets doubled then resistance also gets doubled.
Now when the radius is double then
⇒ `"R"_2 = (rho"l")/"A"`
⇒`"R"_2 = (rhol)/(pi(2"r")^2`
`therefore "R"_2 = 1/4("R")`
So if the radius gets doubled then resistance will be `(1/4)^"th"` of initial resistance.
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