NEET Sample Paper NEET Sample Test Paper-1

  • question_answer If a wire of resistance R is stretched to double its length, then the new resistance is:

    A)  \[4R\]               

    B)  \[2R\]

    C)  R                    

    D)  none of these

    Correct Answer: A

    Solution :

    Initial Resistance \[{{R}_{1}}=R\] Initial length     \[{{l}_{1}}=l\]                               Final lenght       \[{{l}_{2}}=2l\] The volume of wire is given by \[\pi r_{1}^{2}\times l\] .                Since the wire of volume remains same after stretch therefore,             \[\pi r_{1}^{2}\times l=\pi r_{2}^{2}\times 2l\] \[\Rightarrow \]               \[{{r}_{2}}=\frac{{{r}_{1}}}{{{r}_{2}}}\] The resistance of wire is given by \[R=\rho \times \frac{l}{\Delta }=\rho \times \frac{l}{\pi {{r}^{2}}}\] \[\Rightarrow \]\[R\propto \frac{l}{{{r}^{2}}}\] \[\frac{{{R}_{1}}}{{{R}_{2}}}=\frac{{{l}_{1}}/r_{1}^{2}}{{{l}_{2}}/r_{2}^{2}}=\frac{l}{2l}=\frac{{{\left( {{r}_{1}}/\sqrt{2} \right)}^{2}}}{{{\left( {{r}_{1}} \right)}^{2}}}\] \[\Rightarrow \]               \[\frac{{{R}_{1}}}{{{R}_{2}}}=\frac{1}{2}\times \frac{1}{2}=\frac{1}{4}\] \[\Rightarrow \]               \[{{R}_{2}}=4{{R}_{1}}=4R\]            


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