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3. current electricity — Physics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 SciencePhysics3. current electricity1 Mark
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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