Q175 / 180 · KCET 2023 · Physics

A moving coil galvanometer is converted into an ammeter of range 0 to $5 \mathrm{~mA}$. The galvanometer resistance is $90 \Omega$ and the shunt resistance has a value of $10 \Omega$. If there are $\mathbf{5 0}$ divisions in the galvanometer-turned-ammeter on either sides of zero, its current sensitivity is

  • A
    $2 \times 10^4 \mathrm{div} / \mathrm{A}$
  • B
    $1 \times 10^5 \mathrm{~A} / \mathrm{div}$
  • C
    $2 \times 10^4 \mathrm{~A} / \mathrm{div}$
  • Correct answer
    D
    $1 \times 10^5 \mathrm{div} / \mathrm{A}$

Solution

Given, $S=10 \Omega$ $\begin{aligned} & G=90 \Omega \\ & i=5 \times 10^{-3} \mathrm{~A}\end{aligned}$ Number of divisions on one side of zero $=50$ $i_g=\frac{S}{S+G} \times i=\left(\frac{10}{90+10}\right)\left(5 \times 10^{-3}\right)=5 \times 10^{-4} \mathrm{~A}$ Number of divisions per unit current $=\frac{50}{5 \times 10^{-4}}$ $=1 \times 10^{-5} \mathrm{div} / \mathrm{A}$

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

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