$A$ conducting ring of radius $a$ is rotated about a point $O$ on its periphery as shown in the figure in a plane perpendicular to a uniform magnetic field $B$ which exists everywhere. The rotational velocity is $\omega$. Choose the correct statement$(s)$ related to the induced current in the ring.

$A$ part of a complete circuit is shown in the figure. At some instant,the value of current $I$ is $1\, A$ and it is decreasing at a rate of $10^{2}\, A s^{-1}$. The value of the potential difference $V_{P} - V_{Q}$ (in volts) at that instant is:

The adjoining figure shows two different arrangements in which two square wire frames are placed in a uniform constantly decreasing magnetic field $B.$ If $I_1$ and $I_2$ are the magnitudes of induced current in the cases $I$ and $II$,respectively,then

The current $(I)$ in the inductance is varying with time according to the plot shown in the figure. Which one of the following is the correct variation of voltage $(V)$ with time in the coil?

$A$ rectangular loop of sides $12 \text{ cm}$ and $5 \text{ cm}$,with its sides parallel to the $x$-axis and $y$-axis respectively,moves with a velocity of $5 \text{ cm/s}$ in the positive $x$-axis direction in a space containing a variable magnetic field in the positive $z$-direction. The field has a gradient of $10^{-3} \text{ T/cm}$ along the negative $x$-direction and it is decreasing with time at the rate of $10^{-5} \text{ T/s}$. If the resistance of the loop is $6 \text{ m}\Omega$,the power dissipated by the loop as heat is . . . . . . $\times 10^{-9} \text{ W}$.

$A$ coil and a bulb are connected in series with a $DC$ source. $A$ soft iron core is then inserted into the coil. What happens to the intensity of the bulb?