what will be eqn of AC and AV in LC circuits?

Asked by prakasan | 11th Sep, 2010, 12:00: AM

Expert Answer:

Dear Student

You may treat LC circuit as LCR circuit with R being accounted for as resistance offered by the either the load or the connecting wires.
Following is the discussion which leads to the voltage & current values in the LCR circuit.

The voltage phasor in  the LCR circuit will be given by

  V=VR+(VL+VC
Taking the dot product


V.V

gives

Vo2  = (VR)2o + (Vc +VL).(Vc +VL)

= (VR)2o +[(VL)o  - (Vc)o]2

= [R2 +(Xc - XL)2]Io2

From this, we immediately get
peak value of the current as   Io=Vo/Z where

The factor Z is the analog of resistance in a purely resistive circuit, and is called Impedance.

The phase is immediately found from the simple phasor picture
        

If Xc >XL, Φ >0, and the circuit is more Capacitive and if 

 Xc L, Φ <0, the circuit is predominantly Inductive.

 
Hope this clarifies your query.
Regards
Team
Topperlearning

Answered by  | 14th Sep, 2010, 10:30: AM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.