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

Two circular coils $P$ and $Q$ are fixed coaxially and carry currents $I_1$ and $I_2$ respectively.

$A$ conducting square loop initially lies in the $XZ$ plane with its lower edge hinged along the $X$-axis. Only in the region $y \geq 0$,there is a time-dependent magnetic field pointing along the $Z$-direction,$\vec{B}(t) = B_0(\cos \omega t) \hat{k}$,where $B_0$ is a constant. The magnetic field is zero everywhere else. At time $t=0$,the loop starts rotating with constant angular speed $\omega$ about the $X$-axis in the clockwise direction as viewed from the $+X$ axis (as shown in the figure). Ignoring self-inductance of the loop and gravity,which of the following plots correctly represents the induced e.m.f. $(V)$ in the loop as a function of time?

The unit $\text{Wb}/\Omega$ represents which physical quantity?

$A$ 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 . . . . . . $\times 10^{-9} \text{ W}$.

$A$ conducting square loop of side $L$,mass $M$ and resistance $R$ is moving in the $XY$ plane with its edges parallel to the $X$ and $Y$ axes. The region $y \geq 0$ has a uniform magnetic field,$\vec{B}=B_0 \hat{k}$. The magnetic field is zero everywhere else. At time $t=0$,the loop starts to enter the magnetic field with an initial velocity $v_0 \hat{\imath} \text{ m/s}$,as shown in the figure. Considering the quantity $K=\frac{B_0^2 L^2}{RM}$ in appropriate units,ignoring self-inductance of the loop and gravity,which of the following statements is/are correct:
$(A)$ If $v_0=1.5 KL$,the loop will stop before it enters completely inside the region of magnetic field.
$(B)$ When the complete loop is inside the region of magnetic field,the net force acting on the loop is zero.
$(C)$ If $v_0=\frac{KL}{10}$,the loop comes to rest at $t=\left(\frac{1}{K}\right) \ln \left(\frac{5}{2}\right)$.
$(D)$ If $v_0=3 KL$,the complete loop enters inside the region of magnetic field at time $t=\left(\frac{1}{K}\right) \ln \left(\frac{3}{2}\right)$.