Physics - EMI/AC Question with Solution | TestHub

Resistance of the circuit,

$\mathrm{R}={\mathrm{R}}_1+{\mathrm{R}}_2=40\mathrm{ }\mathrm{\Omega }+40\mathrm{ }\mathrm{\Omega }=80\mathrm{ }\mathrm{\Omega }$

Impedance of the circuit,

$\mathrm{Z}=\sqrt{{\mathrm{R}}^2+{\left({\mathrm{X}}_{\mathrm{L}}-{\mathrm{X}}_{\mathrm{C}}\right)}^2}=\sqrt{{\left(80\right)}^2+{\left(100-40\right)}^2}$

$=\sqrt{{\left(80\right)}^2+{\left(60\right)}^2}=100\mathrm{ }\mathrm{\Omega }$

Power factor, $\cos \mathrm{\varphi }=\frac{R}{Z}=\frac{80}{100}=0.8$