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AIIMS 2002
Exam
AIIMS
Year
2002
Subject
Physics
Chapter
Current Electricity

AIIMS 2002 · Physics · Current Electricity

When a wire is stretched and its radius becomes r / 2 , then its...

When a wire is stretched and its radius becomes r/2r / 2, then its resistance will be

Options

  1. A16R16 R
  2. B2R2 R
  3. C4R4 R
  4. D0.

Correct answer

A. 16R16 R

Step-by-step solution

Initial radius of wire, r1=rr_1=r and final radius of wire, r2=r/2=0.5rr_2=r / 2=0.5 r. Since volume of the wire after stretch remains constant, therefore l1A1=l2A2l_1 A_1=l_2 A_2 or \frac{l_1}{l_2}=\frac{A_2}{A_1}=\frac{r_2^2}{r_1^2}=\left(\frac{0.5 r}{r}\right)^2=14.\frac{1}{4} .The resistance (R)=ρlA∝lA(R)=\rho \frac{l}{A} \propto \frac{l}{A}. Therefore R1R2=l1l2×A2A1=14×14=116\frac{R_1}{R_2}=\frac{l_1}{l_2} \times \frac{A_2}{A_1}=\frac{1}{4} \times \frac{1}{4}=\frac{1}{16} or R2=16R1=16R\quad R_2=16 R_1=16 R.
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