Inductive AC Circuit
In Inductive AC circuit only circuit element which is present is inductor.
AC voltage supplied to a inductor:-
- The source of voltage is alternating as is represented as V = Vm sinωt.
- In the circuit there is source voltage(V) and an inductor with inductance = L.
- In this circuit there are no resistors. There is one source EMF i.e. is the source voltage and another emf is self-induced.
- As current is changing therefore the magnetic flux associated with the current also changes.
- According to Faraday’s Lenz’s law whenever there is change in the flux a current is induced or an EMF is induced in the inductor.
- As a result there will be self-induced EMF in the inductor which will oppose the change which is causing it.
- Therefore V + e = 0.
- Where V = source voltage and e = self- induced emf in the inductor L.
- => V - L(dI/dt) = 0 . Using e = -L (dI/dt)
- => Vm sinωt - L(dI/dt) = 0.
- =>dI = (Vm sinωt dt /L)
- Integrating both sides , therefore 0I∫dI = ∫ (Vm sinωt dt /L)
- After simplifying, I = (Vm/L) [ -cosωt/ω] + constant
- I = - (Vm/ ω L) cosωt + 0
- (constant = 0 because as source voltage oscillate symmetrically about 0, therefore current should also oscillate about 0.)
- I = - Im cosωt
- I = Im sin(ωt –(∏/2)) . This is the current which will flow through the circuit.
The current and voltage are not in phase with each other. They are out of phase by (∏/2).
(Circuit diagram containing a voltage source and an inductor).
- Current amplitude Im = (Vm / ω L) .
- In an inductance circuit (ω L) acts as resistance, when compared with I = (V/R). Therefore the resistance of inductive circuit is known as inductive reactance.
- Inductive reactance is the resistance associated with a pure inductive AC circuit.
- It is denoted by XL.
- S.I. unit: ohm(Ω).
- It limits the current flowing through an inductive circuit.
- XL = ω L . => XL ∝ ω and XL ∝ L.
Problem:- A 44 mH inductor is connected to 220 V, 50 Hz ac supply. Determine the RMS value of the current in the circuit.
Inductance of inductor, L = 44 mH = 44 × 10−3 H
Supply voltage, V = 220 V
Frequency, ν = 50 Hz
Angular frequency, ω = 2πν
Inductive reactance, XL = ω L = 2πν L = (2π × 50 × 44 × 10−3) Ω
RMS value of current is given as:
I = (V/XL)
= (220)/(2π × 50 × 44 × 10−3) = 15.92 A
Hence, the rms value of current in the circuit is 15.92 A.
Graphical representation of Voltage & Current
- Voltage and current are represented as:- V = Vm sinωt and I = Im sin(ωt –(∏/2)) respectively. Voltage and current are out of phase by (∏/2).
- Current lags voltage by (∏/2).Current will reach its maximum value after(∏/2).
- Average current over a complete cycle is 0.
- Average voltage over a complete cycle is 0.