Two circuits have a coefficient of mutual induction of $0.09 \ H$. The average $e.m.f.$ induced in the secondary circuit due to a change of current from $0 \ A$ to $20 \ A$ in $0.006 \ s$ in the primary circuit will be:

Two coils $A$ and $B$ are wound on the same iron core as shown in the figure. The number of turns in the coils $A$ and $B$ are $N_A$ and $N_B$ respectively. Identify the correct statement.

$A$ circular wire loop of radius $R$ is placed in the $x$-$y$ plane centered at the origin $O$. $A$ square loop of side $a$ $(a \ll R)$ having two turns is placed with its center at $z = \sqrt{3} R$ along the axis of the circular wire loop,as shown in the figure. The plane of the square loop makes an angle of $45^{\circ}$ with respect to the $z$-axis. If the mutual inductance between the loops is given by $\frac{\mu_0 a^2}{2^{p / 2} R}$,then the value of $p$ is

Two coils $P$ and $Q$ are separated by some distance. When a current of $3\, A$ flows through coil $P$,a magnetic flux of $10^{-3}\, Wb$ passes through $Q$. No current is passed through $Q$. When no current passes through $P$ and a current of $2\, A$ passes through $Q$,the flux through $P$ is:

$X$ and $Y$ are two circuits having a coefficient of mutual inductance $3 \text{ mH}$ and resistances $10 \text{ } \Omega$ and $4 \text{ } \Omega$ respectively. To have an induced current of $60 \times 10^{-4} \text{ A}$ in circuit $Y$,the amount of current to be changed in circuit $X$ in $0.02 \text{ s}$ is: (in $A$)

$A$ varying current at the rate of $3 \, A/s$ in a coil generates an $e.m.f.$ of $8 \, mV$ in a nearby coil. The mutual inductance of the two coils is: