A coil of 'n' turns and resistance $R\,\Omega$ is connected in series with a resistance $R/4$. The combination is moved for time 't' second through flux $\Phi_1$ to $\Phi_2$. The induced current in the circuit is

The coefficient of mutual induction is $3$H and induced e.m.f. across secondary is $4$ kV. Current in primary is reduced from $7$A to $2$A. The time required for the change of current is

A bar magnet falls from a height 'h' through a metal pipe, its acceleration after coming out of pipe is

A series LCR circuit is connected to an a.c. source of $220$ V, $50$ Hz. The circuit contains a resistance $R = 80\,\Omega$, an inductor of inductive reactance $70\,\Omega$ and capacitor of capacitive reactance $130\,\Omega$. The power factor of the circuit is $\dfrac{x}{10}$. The value of x is