Physics - EMI/AC Question with Solution | TestHub

${\text{X}}_{\text{L}}=31\mathrm{ \Omega }\text{, }{\text{X}}_{\text{C}}=25\mathrm{ \Omega }\text{, }\text{R}=8\mathrm{ \Omega }$

Impedance of series$LCR$is

$\text{Z}=\sqrt{\left({\text{R}}^2\right)+{\left({\text{X}}_{\text{L}}-{\text{X}}_{\text{C}}\right)}^2}$

$=\sqrt{{\left(8\right)}^2+{\left(31-25\right)}^2}=\sqrt{64+36}=10\mathrm{ \Omega }$

Power factor,$\text{cos}\varphi =\frac{\text{R}}{\text{Z}}=\frac{8}{10}=\text{0.8}$