Final answer:
The total inductive reactance of three inductors with inductances of 60 mH, 50 mH, and 100 mH connected in series and connected to a 60 Hz source is approximately 78.96 ohms.
Step-by-step explanation:
The inductive reactance of an inductor in an AC circuit is calculated using the formula XL = 2πfL, where f is the frequency in hertz and L is the inductance in henrys. When inductors are connected in series, their total inductance is the sum of their individual inductances. Therefore, the total inductance Ltotal of three inductors with inductances of 60 mH, 50 mH, and 100 mH connected in series is Ltotal = 60 mH + 50 mH + 100 mH = 210 mH.
To find the total inductive reactance for a 60 Hz source, we substitute f = 60 Hz and Ltotal = 210 mH or 0.210 H into our formula: XL = 2π(60)(0.210), which gives us the total inductive reactance in ohms. Performing the calculation, we get XL ≈ 78.96 Ω.