Q123 / 150 · MHT CET 2021 (21 Sep Shift 1) · Physics

In a meter bridge experiment, the balance point is obtained at length $\ell_1 \mathrm{~cm}$ from left end when resistances in the left gap and right gap are $5 \Omega$ and $R \Omega$ respectively. When the resistance $R$ is shunted with equal resistance, the new balance point is at $1.6 \ell_1$. The resistance $\mathrm{R}$ in ohm is

  • A
    25
  • Correct answer
    B
    15
  • C
    10
  • D
    20

Solution

$$ \frac{5}{R}=\frac{\ell_1}{100-\ell_1} $$ When $\mathrm{R}$ is shunted, $$ \begin{aligned} & \frac{5 \times 2}{\mathrm{R}}=\frac{1.6 \ell_1}{100-1.6 \ell_1} \\ & \therefore \frac{5}{\mathrm{R}}=\frac{0.8 \ell_1}{100-1.6 \ell_1} \end{aligned} $$ Equating (1) and (2) and solving we get $\ell_1=25 \mathrm{~cm}$ Putting this in Eq. (1), we get $R=15 \Omega$

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

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