Magnetic Effects & Magnetism

JEE Main level, single correct, medium

187 of 276

Question 187 of 276

In a moving coil galvanometer, two moving coils M1M_1 and M2M_2 have the following particulars :
$\begin{aligned}

& \mathrm{R}_1=5 \Omega, \mathrm{~N}_1=15, \mathrm{~A}_1=3.6 \times 10^{-3} \mathrm{~m}^2, \mathrm{~B}_1=0.25 \mathrm{~T} \\

& \mathrm{R}_2=7 \Omega, \mathrm{~N}_2=21, \mathrm{~A}_2=1.8 \times 10^{-3} \mathrm{~m}^2, \mathrm{~B}_2=0.50 \mathrm{~T}

\end{aligned}$

Assuming that torsional constant of the springs are same for both coils, what will be the ratio of voltage sensitivity of
M1M_1 and M2M_2 ?

Show answer and solution

Answer: (A) 1:11: 1

 Voltage sensitivity =θV=NABcR Ratio ==(N1 A1 B1 N2 A2 B2)R2R1=15×3.6×0.2521×1.8×0.5×75=11\begin{aligned} & \text { Voltage sensitivity }=\frac{\theta}{V}=\frac{N A B}{c R} \\ & \text { Ratio }==\left(\frac{\mathrm{N}_1 \mathrm{~A}_1 \mathrm{~B}_1}{\mathrm{~N}_2 \mathrm{~A}_2 \mathrm{~B}_2}\right) \frac{\mathrm{R}_2}{\mathrm{R}_1}=\frac{15 \times 3.6 \times 0.25}{21 \times 1.8 \times 0.5} \times \frac{7}{5}=\frac{1}{1}\end{aligned}

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