MHTCET 15 Apr 2026 Shift 1 Paper

Concept:In a series LCR circuit, the power factor is the ratio of resistance to the total impedance of the circuit.Explanation:The power factor is given by:$$\cos \phi = \frac{R}{Z}$$where $Z$ is the impedance of the circuit.For a series LCR circuit, impedance is:$$Z = \sqrt{R^2 + (X_L - X_C)^2}$$Here, $R = 80\ \Omega$, $X_L = 70\ \Omega$, and $X_C = 130\ \Omega$.So, the net reactance is:$$X_L - X_C = 70 - 130 = -60\ \Omega$$The negative sign indicates a capacitive circuit, but for impedance we use the square:$$Z = \sqrt{80^2 + (-60)^2} = \sqrt{6400 + 3600}$$$$Z = \sqrt{10000} = 100\ \Omega$$Thus, the power factor is:$$\cos \phi = \frac{80}{100} = 0.8$$Given that the power factor is $\frac{x}{10}$, we equate:$$\frac{x}{10} = 0.8 = \frac{8}{10}$$Therefore, $x = 8$.Answer:The value of $x$ is $8$, which corresponds to option A.