Question

resistance of a wire is 20 ohm what will be new resistance if it is straight uniformly 8 time it original length

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Answer 1

Perfect question:

The resistance of the wire 20 ohm. What will be new resistance ,if it is stretched uniformly 8 times it's original length

AnSwer :

Given :

resistance of wire = 20 Ω

length, l = 8l

To find :

the new resistance

Solution :

we know that,

The resistance of the conductor is directly proportional to its length and inversely proportional to its area of cross section

In other words

${ \bf {R = \rho \dfrac{l}{A}}}$

here, R denotes resistance of the conductor, A denotes area of cross section and l denotes length.

when R = 20Ω

${ \bf {20 = \rho \dfrac{l}{A}}} \: \: \: \: .......(1)$

let the new resistance be R' when length stretches is 8times, l = 8l

${ \bf {R' = \rho \dfrac{l}{A}}}$

${ \bf {R' = \rho \dfrac{8l}{A}}} \: \: \: \: \: .....(2)$

now, substitute (1) in (2)

${ \bf {R' = 8 \times 20}}$

${ \bf {R' = 160 \: \Omega}}$

thus, the new resistance of the wire is 160Ω

Remember !

SI unit of resistance is ohms (Ω)