Two coils A and B are connected in series across a 110V, 60Hz supply. The resistance of coil A is 2 and inductance of coil B is 0.004H. If the input from the supply is 2.4kW and 1.8kVAR, find the inductance of coil A and resistance of coil B. Also calculate the voltage across each coil.
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Expert's answer
2021-02-25T04:10:51-0500
The frequency is 60 Hz, so, the reactance of the second coil is
X2=2πfL2=1.5Ω.
So, since the total voltage is 110 V, the connection is series, and the active power output is 2400 W:
P=R1+R2V2,R2=PV2−R1=3.04Ω.
The voltage across the first one:
V1=IR1=R1+R2VR1=43.7 V,V2=IR2=R1+R2VR2=66.3 V.
Find the power factor:
cosϕ=P2+Q2P=0.8.
The reactance of the first coil can be found from the following:
cosϕ=(R1+R2)2+(X1+X2)2R1+R2,X1=(cosϕR1+R2)2−(R1+R2)2−X2=2.28Ω,L1=2πfX1=0.006 H.
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