A galvanometer of resistance $100\,\Omega $ has $50\, divisions$ on its scale and has sensitivity of $20\,\mu A / division$. It is to be converted to a voltmeter with three ranges, of $0-2\, V$, $0-10\, V$ and $0-20\, V$. The appropriate circuit to do so is
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A circular coil of $500$ turns encloses an area of $0.04 \,m^2.$ A uniform magnetic field of induction $0.25\, Wb/m^2$ is applied perpendicular to the plane of the coil. The coil is rotated by $90^o$ in $0.1$ second at a constant angular velocity about one of its diameters. A galvanometer of resistance $25\Omega$ was connected in series with the the coil. The total charge that will pass through the galvanometer is.......$C$
A galvanometer of resistance $G$ is converted into a voltmeter of range $0-1\, V$ by connecting a resistance $R _{1}$ in series with it. The additional resistance that should be connected in series with $R _{1}$ to increase the range of the voltmeter to $0-2\, V$ will be
To produce a uniform magnetic field directed parallel to a diameter of a cylindrical region, one can use the saddle coils illustrated in figure. The loops are wrapped over a somewhat flattened tube. Assume the straight sections of wire are very long. The end view of the tube shows how the windings are applied. The overall current distribution is the superposition of two overlapping,circular cylinders of uniformly distributed current, one toward you and one away from you. The current density $J$ is the same for each cylinder. The position of the axis of one cylinder is described by a position vector a relative to the other cylinder. The magnetic field inside the hollow tube is.
A particle of mass $m = 1.67 \times 10^{-27}\, kg$ and charge $q = 1.6 \times 10^{-19} \, C$ enters a region of uniform magnetic field of strength $1$ $tesla$ along the direction shown in the figure. The speed of the particle is $10^7\, m/s.$ The magnetic field is directed along the inward normal to the plane of the paper. The particle enters the field at $C$ and leaves at $D.$ Then the angle $\theta$ must be :-.........$^o$
Due to the flow of current in a circular loop of radius $R$, the magnetic field produced at the centre of the loop is $B$. The magnetic moment of the loop is :-
A long straight wire along the $z-$ axis carries a current $I$ in the negative $z$ direction. The magnetic field vector $\vec B$ at a point having coordinates $(x, y)$ in the $z = 0$ plane is