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ICSE Class 12-science Answered

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 | 24 Jul, 2019, 11:25: AM

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 Thiyagarajan K | 24 Jul, 2019, 13:47: PM

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