An inductance coil has a reactance of . When an AC signal of frequency is applied to the coil, the applied voltage leads the current by . The self-inductance of the coil is:
Step 1: Given data and assumption.
Impudence of the coil,
Frequency,
Current leads the voltage by an angle,
Step 2: Finding the self-inductance of the coil.
Since, It is clear from the given data that the inductance is not pure inductance. The given coil behaves as a series combination of L and R.
Therefore,
The applied voltage leads the current by
Where, is inductive reactance.
……
Now,
We know that
Impedance of the coil,
…..
As we know that,
where is angular frequency
Hence, option D is correct.