Two coil $A$ and $B$ have coefficient of mutual inductance $M=2 \mathrm{H}$. The magnetic flux passing through coil $A$ changes by $4$ $\mathrm{Wb}$ in $10 \mathrm{s}$ due to the change in current in $B$. Then

An electric current $i_1$ can flow either direction through loop $\left(1\right)$and induced current $i_2$ in loop $\left(2\right)$. Positive $i_1$ is when current is from '$a$' to ' $b$ ' in loop $\left(1\right)$ and positive $i_2$ is when the current is from '$c$' to '$d$' in loop $\left(2\right)$. In an experiment, the graph of $i_2$ against time '$t$' is as shown below,
which one(s) of the following graphs could have caused $i_2$ to behave as give above

Two infinitcly long conducting parallel rails are connected through a capacitor $C$ as shown in figure. A conductor of length $l$ is moved with constant speed $v_0$. Which of the following graph truly depicts the variation of current through the conductor with time?

Two conducting rings $P$ and $Q$ of radii and $r$ and $2r$ rotate uniformly in opposite directions with centre of mass velocities $2v$ and $v$ respectively on a conducting surface $S$. There is a uniform magnetic field of magnitude $B$ perpendicular to the plane of the rings. The potential difference between the highest points of the two rings is

A triangular wire frame (each side $=2 \mathrm{m}$) is placed in a region of time variant magnetic field $\frac{dB}{dt}=\sqrt{3} \mathrm{T} {\mathrm{s}}^{-1}$. The magnetic field is perpendicular to the plane of the triangle and its centre coincides with the centre of triangle. The base of the triangle $AB$ has a resistance $1\Omega$ while the other two sides have resistance $2\Omega$ each. The magnitude of potential difference between the points $A$ and $B$ will be

The ratio of time constant in charging and discharging in the circuit shown in figure is

For $L-R$ circuit, the time constant is equal to