A wire of resistance R₁ is drawn out so that its length is increased by twice of its original length. The ratio of new resistance to original resistance is :

The current sensitivity of a galvanometer can be increased by :

(A) decreasing the number of turns

(B) increasing the magnetic field

(C) decreasing the area of the coil

(D) decreasing the torsional constant of the spring

Choose the most appropriate answer from the options given below :

As shown in the figure, a metallic rod of linear density $$0.45 \mathrm{~kg} \mathrm{~m}^{-1}$$ is lying horizontally on a smooth inclined plane which makes an angle of $$45^{\circ}$$ with the horizontal. The minimum current flowing in the rod required to keep it stationary, when $$0.15 \mathrm{~T}$$ magnetic field is acting on it in the vertical upward direction, will be :

{Use $$g=10 \mathrm{~m} / \mathrm{s}^{2}$$}

The equation of current in a purely inductive circuit is $$5 \sin \left(49\, \pi t-30^{\circ}\right)$$. If the inductance is $$30 \,\mathrm{mH}$$ then the equation for the voltage across the inductor, will be :

$$\left\{\right.$$ Let $$\left.\pi=\frac{22}{7}\right\}$$