Two inductors $L_1$ (inductance $1 \text{ mH}$,internal resistance $3 \text{ } \Omega$) and $L_2$ (inductance $2 \text{ mH}$,internal resistance $4 \text{ } \Omega$),and a resistor $R$ (resistance $12 \text{ } \Omega$) are all connected in parallel across a $5 \text{ V}$ battery. The circuit is switched on at time $t=0$. The ratio of the maximum to the minimum current $(I_{\max} / I_{\min})$ drawn from the battery is:

As per the given figure,if $\frac{ dI }{ dt } = -1 \text{ A/s}$,then the value of $V_{AB}$ at this instant will be $.......... \text{ V}$.

The current $i$ in an inductance coil varies with time $t$ according to the following graph. Which one of the following plots shows the variations of voltage $V$ in the coil?

$A$ conducting loop in the shape of a right-angled isosceles triangle of height $10 \ cm$ is kept such that the $90^{\circ}$ vertex is very close to an infinitely long conducting wire (see the figure). The wire is electrically insulated from the loop. The hypotenuse of the triangle is parallel to the wire. The current in the triangular loop is in counterclockwise direction and increases at a constant rate of $10 \ As^{-1}$. Which of the following statement$(s)$ is(are) true?
$(A)$ The magnitude of induced emf in the wire is $\left(\frac{\mu_0}{\pi}\right) \ V$
$(B)$ If the loop is rotated at a constant angular speed about the wire,an additional emf of $\left(\frac{\mu_0}{\pi}\right) \ V$ is induced in the wire
$(C)$ The induced current in the wire is in the opposite direction to the current along the hypotenuse
$(D)$ There is a repulsive force between the wire and the loop

Shown in the figure is a circular loop of radius $r$ and resistance $R$. $A$ variable magnetic field of induction $B = B_0 e^{-t}$ is established inside the coil. If the key $K$ is closed,the electrical power developed right after closing the switch is equal to

The current $i$ in an induction coil varies with time $t$ according to the graph shown. Which of the following graphs shows the induced $emf$ $(e)$ in the coil with time?