A conducting loop of finite resistance lies on the $x-y$ plane. There is a constant magnetic field in the $z$ direction. The area of the loop varies with time $t$, as $A=A_0(1+\sin t)$ in appropriate units. The figure that correctly indicates the qualitative behaviour of the power $P$ dissipated in the loop as a function of time is:

A rectangular wire loop of sides 8 cm and 3 cm with a small cut, is moving out of a region of uniform magnetic field of magnitude 0.3 T directed normal to the plane of the loop. The emf developed across the cut, if the velocity of the loop is $2 \mathrm{~cm} \mathrm{~s}^{-1}$, in a direction normal to the shorter side of the loop, will be :

$A B$ is a part of an electrical circuit (see figure). The potential difference " $V_A-V_B$ ", at the instant when current $i=2 \mathrm{~A}$ and is increasing at a rate of $1 \mathrm{amp} /$ second is:

Let us consider two solenoids $$A$$ and $$B$$, made from same magnetic material of relative permeability $$\mu_r$$ and equal area of cross-section. Length of $$A$$ is twice that of $$B$$ and the number of turns per unit length in $$A$$ is half that of $$B$$. The ratio of self inductances of the two solenoids, $$L_A: L_B$$ is