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  • A wire 2m long has a resistance of 2. If it is uniformly stretched so that its length increases by 30%, then its r

A wire 2m long has a resistance of 2\Omega. If it is uniformly stretched so that its length increases by 30%, then its resistance will increase by:

Option: 1

30%


Option: 2

60%


Option: 3

69%


Option: 4

34%


Answers (1)

l{}' = l + \frac{30l}{100} = \frac{130l}{100} = 1.30 l

Let the new area of cross-section = A{}'

So, Ald = A{}'l{}'d

\Rightarrow A{}' = \frac{Al}{l{}'} = \frac{A * l}{1.30l} = \frac{100}{130} A     and

    R = \frac{\rho (\frac{130}{100} l)}{\frac{100}{130}A} = \frac{\rho l}{A} * (\frac{130}{100})^2 = 1.69 R

% increase in resistance 

    = \frac{R{}' - R}{R} * 100% = \frac{(1.69 - 1) R}{R} * 100

    = 69%

Posted by

Sumit Saini

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