Alternating current of peak value $(\frac{2}{\pi}) \ A$ flows through the primary coil of a transformer. The coefficient of mutual inductance between the primary and secondary coil is $1 \ H$. The peak e.m.f. induced in the secondary coil is (Frequency of a.c. $= 50 \ Hz$) (in $V$)

An electric current $i_1$ can flow in either direction through loop $(1)$ and induces a current $i_2$ in loop $(2)$. Positive $i_1$ is defined when the current flows from $'a'$ to $'b'$ in loop $(1)$,and positive $i_2$ is defined when the current flows from $'c'$ to $'d'$ in loop $(2)$. 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 given above?

$A$ primary coil and a secondary coil are placed close to each other. $A$ current, which changes at the rate of $25 \, A$ in a millisecond, is present in the primary coil. If the mutual inductance is $92 \times 10^{-6} \, H$, then the value of the induced emf in the secondary coil is:

The dimension of mutual inductance 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 $A$)

Two coils,$X$ and $Y$,are kept in close vicinity of each other. When a varying current,$I(t)$,flows through coil $X$,the induced emf $(V(t))$ in coil $Y$ varies in the manner shown in the figure. The variation of $I(t)$ with time can then be represented by the graph labeled as: