Question

Mcg has no. Of turns 24 . Area =20x10^-3 ,B =0.2 T , R= 14 ohm.
Indicate the way to increase current sensitivity by 25% .on doing so the resistance increase to 21 ohm. Is the voltage sensitivity of the modified metre greater or less than the original meter

Answer 1

Dear student
$$\begin{gathered} Torqueonthecoilis \\ T=NiAB\sin \theta \\ k{\theta }_0=NiAB\sin \theta \\ inradialmagneticfield\theta =90° \\ k{\theta }_0=NiAB\sin 90° \\ k{\theta }_0=NiAB \\ currentsensitivityis{s}_v=\frac{{\theta }_o}{i}=\frac{NAB}{k} \\ ifweincreasethecurrentsensitivityby25percentthiscanbedonebyincrea\sin gthenumberofturnsto1.25timesandkeepingallotherfactorscons\tan t. \\ Percentagechangeincurrentsensitivityis \\ {s}_v=\frac{NAB}{k}=cN \\ \left(\frac{s_{v2}-s_{v1}}{s_{v1}}\right)\times 100=\left(\frac{c{N}_2-c{N}_1}{c{N}_1}\right)\times 100=(\frac{N_2}{N_1}-1)\times 100=(\frac{1.25N_1}{N_1}-1)\times 100=25 \\ \frac{{\theta }_o}{i}=\frac{NAB}{k} \\ \frac{{\theta }_{o}R}{V}=\frac{NAB}{k} \\ Voltagesensitivityis\frac{{\theta }_o}{V}=\frac{NAB}{kR} \\ lengthofonecircularturnis2\pi r \\ lengthofonecircularturnisl=2\pi r\times N \\ Resis\tan ceR=\frac{\rho l}{A}=\frac{\rho \times 2\pi r\times N}{A} \\ \frac{R}{N}=\frac{\rho \times 2\pi r}{A} \\ Asvoltagesensitivitydependsonratioof\frac{R}{N}sowithincreaseinresis\tan cethereisnochangeinvoltagesensitivity. \\ Regards \end{gathered}$$