Two coils $A$ and $B$ having turns $300$ and $600$ respectively are placed near each other. On passing a current of $3.0 \ A$ in coil $A$, the magnetic flux linked with coil $A$ is $1.2 \times 10^{-4} \ Wb$ and with coil $B$ it is $9.0 \times 10^{-5} \ Wb$. The mutual inductance of the system is:

Two coils have a mutual inductance of $0.005 \text{ H}$. The current changes in the first coil according to equation $I = I_0 \sin \omega t$, where $I_0 = 10 \text{ A}$ and $\omega = 60\pi \text{ rad s}^{-1}$. The maximum value of e.m.f. in the second coil in volt will be (in $\pi$)

Two concentric circular coils having radii $r_1$ and $r_2$ $(r_2 \ll r_1)$ are placed co-axially with centres coinciding. The mutual inductance of the arrangement is (Both coils have single turn, $\mu_0$ = permeability of free space)

With the decrease of current in the primary coil from $2\,A$ to zero in $0.01\,s$,the $emf$ generated in the secondary coil is $1000\,V$. The mutual inductance of the two coils is......$H$.

Two coils have a mutual inductance of $0.005\,H$. The current in the first coil changes according to the equation $I = I_0 \sin \omega t$,where $I_0 = 10\,A$ and $\omega = 100\pi \,rad/s$. The maximum value of $emf$ in the second coil will be: (in $\pi \,V$)

The inductors of two $LR$ circuits are placed next to each other,as shown in the figure. The values of the self-inductance of the inductors,resistances,mutual-inductance,and applied voltages are specified in the given circuit. After both the switches are closed simultaneously,the total work done by the batteries against the induced $EMF$ in the inductors by the time the currents reach their steady-state values is . . . . $mJ$.