Theo gia thiet thi khi noi tat tu dong dien trong hai truong hop vuong pha voi nhau nen:
$\frac{R}{Z_{L}}=\frac{Z_{C}-Z_{L}}{R}=>Z_{C}-Z_{L}=\frac{R^2}{Z_{L}}$
Khi noi tat tu ta cung co dien ap hieu dung giua 2 dau dien tro R tang 2 lan nen:
$2\sqrt{R^2+Z^2_{L}}=\sqrt{R^2+(Z_{L}-Z_{C})^2}$
$<=>4R^2+4Z^2_{L}=R^2+\frac{R^4}{Z^2_{L}}$
$<=>R^4-3R^2.Z^2_{L}-4Z^4_{L}=0$
Day la pt dang cap dang co ban de dang suy ra
$R=2Z_{L}$
Khi do de dang tim dk he so cong suat cua doan mach luc sau
$cos\varphi=\frac{R}{\sqrt{R^2+Z^2_{L}}}\frac{R}{\sqrt{R^2+\frac{R^2}{4}}}=\frac{2}{\sqrt{5}}$