XL = 2*pi*f*L = 2*pi*60*L
power factor , cos(theta) = R/Z = 0.750
=> impedence , Z = R/0.750 = [R^2 + (XL)^2]^0.5
=> (1.33R)^2 = R^2 + (XL)^2
=> 0.768R^2 = (XL)^2 = (2*pi*60*L)^2
=> L = 2.32R*10^-3
now f = 180 Hz
=> XL = 2*pi*180*L = 180*2*pi*2.32*R*10^-3 = 2.62R
=> impedence . Z =[ R^2 + (XL)^2]^0.5 = [R^2 + (2.62R)^2]^0.5 = 2.80R
=> power factor , cos(theta) = R/Z = R/2.80R = 0.357
Ans: .354 A coil of resistance R, inductance L, and negligible capacitance has a power factor...
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