An impedance coil has a resistance of 20 ohms and an inductive reactance of 40 ohms. For what value of series resistance will the overall power factor of the circuit be 0.3?.
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Ans.10 ohms
pf = cos φ = 0.3
sin φ = √1-0.3^2 = 0.954 = X/Z
Z = X/sin φ = 40/0.954 = 41.93 ohm
0.3 = R/Z
R = Z*0.3 = 41.93*0.3 = 12.58 ohm....10 ohm is wrong !!!
cos phi = 0.3 ----> tan phi = 3.179
tan phi = XL / R
3.179 = 40 / R
R = 12.57 ohms
you should connect a 33.83 ohms across 20 ohms
if we accept answer...pf will be 0.6
Comments
pf = cos φ = 0.3
sin φ = √1-0.3^2 = 0.954 = X/Z
Z = X/sin φ = 40/0.954 = 41.93 ohm
0.3 = R/Z
R = Z*0.3 = 41.93*0.3 = 12.58 ohm....10 ohm is wrong !!!
cos phi = 0.3 ----> tan phi = 3.179
tan phi = XL / R
3.179 = 40 / R
R = 12.57 ohms
you should connect a 33.83 ohms across 20 ohms
if we accept answer...pf will be 0.6