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STD 12 - 3. current electricity — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 3. current electricity4 Marks
MCQ
A thick wire is stretched so that its length become two times. Assuming that there is no change in its density, then what is the ratio of change in resistance of wire to the initial resistance of wire
  • A
    $2:1$
  • B
    $4:1$
  • ✓
    $3:1$
  • D
    $1:4$
✓

Answer

Correct option: C.
$3:1$
c
(c) In stretching $R \propto {l^2}$ $ \Rightarrow $ $\frac{{{R_2}}}{{{R_1}}} = \frac{{{l_2}^2}}{{{l_1}^2}}$ $ \Rightarrow $ $\frac{{{R_2}}}{{{R_1}}} = {\left( {\frac{2}{1}} \right)^2}$

$ \Rightarrow $${R_2} = 4{R_1}$. Change in resistance $ = {R_2} - {R_1} = 3{R_1}$

Now, $\frac{{{\rm{Change}}\,\,{\rm{in}}\,\,{\rm{resistance}}}}{{{\rm{Original}}\,\,{\rm{resistance}}}} = \frac{{3{R_1}}}{{{R_1}}} = \frac{3}{1}$

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