Two galvanometers ' $A$ ' and 'B' require currents of $4 \mathrm{~mA}$ and $7 \mathrm{~mA}$, respectively to…

Two galvanometers ' $A$ ' and 'B' require currents of $4 \mathrm{~mA}$ and $7 \mathrm{~mA}$, respectively to produce the same deflection of 20 divisions. If ' $\mathrm{S}_{A}{ }^{\prime}$ and ${ }^{\prime} \mathrm{S} \mathrm{B}^{\prime}$ are their sensitivities, respectively, then
  1. $\mathrm{S}_{\mathrm{A}}>\mathrm{S}_{\mathrm{B}}$
  2. $\mathrm{S}_{\mathrm{A}}=\mathrm{S}_{\mathrm{B}}=\frac{4}{7}$
  3. $\mathrm{~S}_{\mathrm{B}}=\frac{7}{4}=\mathrm{S}_{\mathrm{A}}$
  4. $\mathrm{S}_{\mathrm{A}} < \mathrm{S}_{\mathrm{B}}$

Solution

$\begin{aligned} \text { sensitivity } \mathrm{S} &=\frac{\theta}{\mathrm{I}} \\ \frac{\mathrm{S}_{\mathrm{A}}}{\mathrm{S}_{\mathrm{B}}} &=\frac{\mathrm{I}_{\mathrm{B}}}{\mathrm{I}_{\mathrm{A}}}=\frac{7}{4} \\ \therefore \mathrm{S}_{\mathrm{A}}>\mathrm{S}_{\mathrm{B}} & \end{aligned}$

Asked in: MHT CET 2020 (19 Oct Shift 2)

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