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:

The coefficient of mutual induction is $2 \text{ H}$ and the induced e.m.f. across the secondary is $2 \text{ kV}$. The current in the primary is reduced from $6 \text{ A}$ to $3 \text{ A}$. The time required for the change of current is:

The planar concentric rings of metal wire having radii $r_1$ and $r_2$ (with $r_1 > r_2$) are placed in air. The current $I$ is flowing through the coil of larger radius. The mutual inductance between the coils is given by $(\mu_0 = \text{permeability of free space})$

$A$ current $I = 10 \sin(100 \pi t) \text{ A}$ is passed in a coil, which induces a maximum emf of $5 \pi \text{ V}$ in a neighboring coil. The mutual inductance of the two coils is: (in $\text{ mH}$)

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 ($\mu_0 =$ permeability of free space) (Both coils have single turn).

Mutual inductance of two coils can be increased by