(a) (i) (1) What is meant by current sensitivity of a galvanometer? Mention the factors on which it depends. (2) A galvanometer of resistance G is…

What is meant by current sensitivity of a galvanometer ? Mention the factors on which it depends.

A galvanometer of resistance G is converted into a voltmeter of range ( $\displaystyle 0-\mathrm{V}$ ) by using a resistance R . Find the resistance, in terms of $\displaystyle R$ and $\displaystyle G$, required to convert it into a voltmeter of range $\displaystyle \left(0-\frac{\mathrm{V}}{2}\right)$.

The magnetic flux through a coil of resistance $\displaystyle 5 \Omega$ increases with time as : \[\phi=\left(2.0 \mathrm{t}^{3}+5.0 \mathrm{t}^{2}+6.0 \mathrm{t}\right) \mathrm{mWb} \] Find the magnitude of induced current through the coil at $\displaystyle \mathrm{t}=2 \mathrm{~s}$.

A rectangular coil of N turns and area of cross-section A is rotated at a steady angular speed $\displaystyle \omega$ in a uniform magnetic field. Obtain an expression for the emf induced in the coil at any instant of time.

Two coplanar and concentric circular loops $\displaystyle \mathrm{L}_{1}$ and $\displaystyle \mathrm{L}_{2}$ are placed coaxially with their centres coinciding. The radii of $\displaystyle \mathrm{L}_{1}$ and $\displaystyle \mathrm{L}_{2}$ are $\displaystyle 1$ cm and $\displaystyle 100$ cm respectively. Calculate the mutual inductance of the loops. (Take $\displaystyle \pi^{2}=10$ )