A coil draws a current of 1.0 ampere and a power of 100 watt from an A.C. source of 110 volt and 5√22/π hertz. Find the inductance and resistance of the coil.

 

Why can't I use P=VI here, and how can I determine when to use P=VI or P=I^2 R or P=V^2 / R

Asked by shaswattafs | 10th Jun, 2021, 06:21: PM

Expert Answer:

Formulas for power , i.e., P = V × I , P  = V2 / R and P  =  I2 R are used for DC circuits.

Above formulas are aslo used in AC circuits , if the AC circuits has only resistive loads like filament bulbs and heating coils.
 
In DC circuits or AC circuits with purely resistive loads , resistance of the circuit decides the current in the circuit and power dissipation.
 
When inductance and capacitance are present in AC circuit, then current and power dissipation depends on the impedence of the AC circuit .
 
Impedence of AC circuit is equivalenet of resistance of DC circuit, but impedence depends on frequency of alternating voltage source.
 
Impedence Z of AC circuit is given as , 
 
begin mathsize 14px style Z space equals space square root of R squared space plus space open parentheses X subscript C space minus space X subscript L close parentheses squared end root end style
where R is resistance , XC = 1/( C ω ) is capacitive reactance  , C is capacitance and ω = ( 2πf ) is angular frequency if f is frequency of alternating voltage source and  XL = ( L ω ) is inductive reactance if L is inductance   
 
Hence RMS Current in AC voltage source ,  Irms = Vrms / Z 
 
Power  P = begin mathsize 14px style I subscript r m s end subscript superscript 2 end style Z 

Answered by Thiyagarajan K | 10th Jun, 2021, 07:13: PM