Q125 / 200 · NEET 2023 (Manipur) · Physics

A certain wire $A$ has resistance $81 \Omega$. The resistance of another wire $B$ of same material and equal length but of diameter thrice the diameter of $A$ will be

  • A
    $729 \Omega$
  • B
    $243 \Omega$
  • C
    $81 \Omega$
  • Correct answer
    D
    $9 \Omega$

Solution

We know that, $R=\frac{\rho l}{A}$, where $A=\frac{\pi}{4} d^2$ $\begin{aligned} & \Rightarrow 81=\frac{\rho \times I}{\frac{\pi}{4} d^2}, \text { also, } R^{\prime}=\frac{\rho \times I}{\frac{\pi}{4} \times(3 d)^2}=\frac{\rho l}{\frac{\pi}{4} \times 9 d^2} \\ & \Rightarrow R^{\prime}=\frac{R}{9}=\frac{81}{9}=9 \Omega\end{aligned}$

Hence, the correct answer is option: 'D'.

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