将一感性负载接到频率f=50HZ交流电流上,功率因数cosφ=0.5,若将电源频率变为100HZ,则功率因数变为?球用高中知识

Question

将一感性负载接到频率f=50HZ交流电流上,功率因数cosφ=0.5,若将电源频率变为100HZ,则功率因数变为____?
球用高中知识

Answer 1

感性负载等效为电感和电阻串联.
cosφ = R / Z = 0.5
φ = 60°
XL / R = tan 60° = √3
XL= 2πFL,XL ' = 2XL (XL' 是100Hz的感抗)
XL' / R = 2XL / R = 2√3
XL' = 2√3 * R
cosφ’ = R / Z‘ =R / √ (R^2+XL’ ^2) = 1/√13 = 0.277