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Home / Doubts and Solutions/ICSE/Class 12 Science/Physics

A coil takes a current of 2.0A and 200 watt power from an alternating current source of 220 volt , 50 Hertz . Calculate the resistance and inductance of the coil 

Asked by hasnain.hossain121 24th July 2019, 11:25 AM
Answered by Expert
Answer:
Power P in AC circuit that contains resistance and Inductance,
 
P = V × I ×cosφ  = I2×z×cosφ ..................... (1)
 
where V and I are voltage and current, z is impedence and φ is phase angle
 
we get phase angleφ (power factor cosφ ) and impedence z, by substituting given power,
Voltage and current from eqn.(1)
 
cosφ = P/(V×I) = 200/(220×2) = 5/11 .......................(2)
 
z = P/(I2 × cosφ ) = ( 200×11 )/(2×2×5) = 110 Ω ......................(3)
 
phase angle φ = tan-1(Lω/R) ,  Hence  Lω/R  = tanφ ≈ 1.96  or  Lω = 1.96×R  ...............(4)
 
impedence z = begin mathsize 12px style square root of R squared plus left parenthesis L omega right parenthesis squared end root space equals space 110 space capital omega end style,     Hence  R2 + L2 ω2 = 110×110 ...............(5)
using eqn.(4) and eqn.(5),   R2 + (1.96×R)2 = 4.84 R2 = 110×110   or   R = 50 Ω ..................(6)
 
using eqn.(5),  begin mathsize 12px style L space equals space square root of fraction numerator 110 squared space minus space 50 squared over denominator 4 straight pi squared cross times 50 cross times 50 end fraction end root space almost equal to space 0.3 space H end style
 
Answered by Expert 24th July 2019, 1:47 PM
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