Class 12 Physics Alternating Current | Inductive AC Circuit |

**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 = V
_{m}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)
- => V
_{m}sinωt - L(dI/dt) = 0. - =>dI = (V
_{m}sinωt dt /L) - Integrating both sides , therefore
_{0}^{I}∫dI = ∫ (V_{m}sinωt dt /L) - After simplifying, I = (V
_{m}/L) [ -cosωt/ω] + constant - I = - (V
_{m}/ ω L) cosωt + 0- (constant = 0 because as source voltage oscillate symmetrically about 0, therefore current should also oscillate about 0.)

**I = - I**_{m}cosωt- where Im = (V
_{m}/ ω L) **I = I**This is the current which will flow through the circuit._{m}sin(ωt –(∏/2)) .

__Conclusion__**:**-

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).

** **

__Inductive Reactance__

- Current amplitude I
_{m}= (V_{m }/ 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 X
_{L}. - S.I. unit: ohm(Ω).
- It limits the current flowing through an inductive circuit.
**X**. => X_{L}= ω L_{L }∝ ω and X_{L }∝ 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.

** Answer**:-

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, X_{L} = ω L = 2πν L = (2π × 50 × 44 × 10^{−3}) Ω

RMS value of current is given as:

I = (V/X_{L})

= (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 = V
_{m}sinωt and I = I_{m}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.

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