Two different coils have self-inductance $8 \ mH$ and $2 \ mH$. The current in both coils is increased at the same constant rate. The ratio of the induced $emf$s in the coils is

$A$ coil and a bulb are connected in series with a $12 \,V$ direct current $(DC)$ source. $A$ soft iron core is now inserted into the coil. Then,

$A$ circuit has self-inductance $L$ and carries a current $I$. To prevent sparking when the circuit is switched off,a capacitor which can withstand potential difference $V$ is used. The least capacitance is

$A$ varying current in a coil changes from $10 \,A$ to zero in $1.5 \,s$. If the average emf induced in the coil is $200 \,V$, the self-inductance of the coil is (in $\,H$)

With the help of $L = \frac{N\phi}{I}$ and $\varepsilon = -L\frac{dI}{dt}$,give two definitions of self-inductance.

$A$ long solenoid has $500$ turns. When a current of $2 \, A$ is passed through it,the resulting magnetic flux linked with each turn of the solenoid is $4 \times 10^{-3} \, Wb$. The self-inductance of the solenoid is ....... $H$.