$A$ coil is wound as a transformer of rectangular cross-section. If all the linear dimensions of the transformer are increased by a factor of $2$ and the number of turns per unit length of the coil remains the same,the self-inductance increases by a factor of:

$A$ $30\text{ cm}$ long solenoid has $10$ turns per cm and area of $5\text{ cm}^2$. The current through the solenoid coil varies from $2\text{ A}$ to $4\text{ A}$ in $3.14\text{ s}$. The e.m.f. induced in the coil is $\alpha \times 10^{-5}\text{ V}$. The value $\alpha$ is . . . . . . .

If $N$ is the number of turns in a coil,the value of self-inductance varies as

An air-cored solenoid with length $20 \, cm$,area of cross-section $20 \, cm^2$,and number of turns $400$ carries a current of $2 \, A$. The current is suddenly switched off within $10^{-3} \, s$. The average back $emf$ induced across the ends of the open switch in the circuit is (ignore the variation in magnetic field near the ends of the solenoid) ........ $V$.

$A$ current $I$ produces a magnetic flux $\phi$ per turn in a coil of $n$ turns. The self-inductance of the coil is $L$. The relation between them is:

$A$ coil of self-inductance $L$ is connected in series with a bulb and an a.c. source. Brightness of the bulb decreases when