In a series LCR circuit, the total voltage (V) is the phasor sum of the voltages across the components. Since the voltage across the inductor ($V_L$) and the capacitor ($V_C$) are $180^\circ$ out of phase, the net reactive voltage is $V_L - V_C$ (or $V_C - V_L$). The voltage across the resistor ($V_R$) is $90^\circ$ out of phase with the net reactive voltage. Using the values given: $V_R = 80$ V, $V_C = 40$ V, $V_L = 100$ V. The net supply voltage $V$ is given by $V = \sqrt{V_R^2 + (V_L - V_C)^2} = \sqrt{80^2 + (100 - 40)^2} = \sqrt{80^2 + 60^2} = \sqrt{6400 + 3600} = \sqrt{10000} = 100$ V. The power factor ($\cos \phi$) is defined as the ratio of resistance to impedance ($R/Z$) or equivalently the ratio of the potential difference across the resistor to the total potential difference ($V_R/V$) . Power Factor = $V_R / V = 80 / 100 = 0.8$.