AC Through Pure Inductance Alone
Whenever an alternating voltage is applied to a purely inductive coil (AC Through Pure Inductance Alone), a back e.m.f. is produced due to the self-inductance of the coil (Refer Article – AC Through Pure Ohmic Resistance Alone). The back e.m.f., at every step, opposes the rise or fall of current through the coil. As there is no ohmic voltage drop, the applied voltage has to overcome this self-induced e.m.f. only. So at every step
Hence, the equation of the current becomes i = Im sin (ωt − π/2).
So, we find that if applied voltage is represented by v = Vm sin ωt, then current flowing in a purely inductive circuit is given by
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Clearly, the current lags behind the applied voltage by a quarter cycle (Figure B & C) or the phase difference between the two is π/2 with voltage leading.
Vectors are shown in Figure (A) where voltage has been taken along the reference axis. We have seen that Im = Vm/ωL = Vm/XL.
Here ‘ωL’ plays the part of ‘resistance’. It is called the (inductive) reactance XL of the coil and is given in ohms if L is in henry and ω is in radian/second.
Now, XL = ωL = 2πfL ohm. It is seen that XL depends directly on frequency of the voltage. Higher the value of f, greater the reactance offered and vice-versa.
Read article – self-inductance
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