AC circuit with an inductor

Let alternating emf , e = eosinωt

L = inductance in an ac circuit

$ \displaystyle e = e_0 sin\omega t = L \frac{di}{dt} $

$ \displaystyle \frac{di}{dt} = \frac{e_0}{L}sin \omega t $

$ \displaystyle i= \frac{e_0}{L} \int sin\omega t dt $

$ \displaystyle i= -\frac{e_0}{\omega L} cos \omega t $

$ \displaystyle i= -\frac{e_0}{X_L} cos \omega t $

where XL = ω L is known as inductive reactance

i= − i0 cos ωt

i= i0 sin (ωt − π/2)

where i0 = e0/XL

In an inductor voltage leads the current by π/2

Also Read :

→Mean value & RMS Value of A.C
→ AC circuit with a Resistor
→ AC circuit with a capacitor
→ L-C-R Series Circuit
→ Power in an a.c. circuit
→ Choke Coil
→ Transformer
→ A . C . Generator

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