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JIPMER 2010
Exam
JIPMER
Year
2010
Subject
Physics
Chapter
Current Electricity

JIPMER 2010 · Physics · Current Electricity

A uniform wire of resistance R and length L is cut into four equal...

A uniform wire of resistance RR and length LL is cut into four equal parts, each of length L/4L / 4, which are then connected in parallel combination. The effective resistance of the combination will be

Options

  1. ARR
  2. B4R4 R
  3. CR4\frac{R}{4}
  4. DR16\frac{R}{16}

Correct answer

D. R16\frac{R}{16}

Step-by-step solution

R=ρlA or  R∝l∴R1R2=l1l2=LL/4=4 or R2=R4(∵R1=R)\begin{aligned} & R=\frac{\rho l}{A} \text{\text{ or } } R \propto l \\ & \therefore \quad \frac{R_1}{R_2}=\frac{l_1}{l_2}=\frac{L}{L / 4}=4 \\ & \text{ or } \quad R_2=\frac{R}{4} \quad\left(\because R_1=R\right) \\ & \end{aligned} In parallel combination of such four resistances. or 1R′=1R2+1R2+1R2+1R2\frac{1}{R^{\prime}}=\frac{1}{R_2}+\frac{1}{R_2}+\frac{1}{R_2}+\frac{1}{R_2} or 1R′=1R/4+1R/4+1R/4+1R/4or1R′=4R+4R+4R+4Ror1R′=16RorR′=R16\quad \frac{1}{R^{\prime}}=\frac{1}{R / 4}+\frac{1}{R / 4}+\frac{1}{R / 4}+\frac{1}{R / 4} or \frac{1}{R^{\prime}}=\frac{4}{R}+\frac{4}{R}+\frac{4}{R}+\frac{4}{R} or \frac{1}{R^{\prime}}=\frac{16}{R} or \quad R^{\prime}=\frac{R}{16}
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