Two identical coils each having inductance L are placed together on the same core. If an overall inductance of $$\alpha$$L is obtained by interconnecting these two coils, the minimum value of $$\alpha$$ is ________.

Find the transformer ratios a and b that the impedance (Z_in) is resistive and equal 2.5 Ω when the network is excited with a sine wave voltage of angular frequency of 5000 rad/s.

The current i (in Ampere) in the 2 Ω resistor of the given network is _________.

A capacitive voltage divider is used to measure the bus voltage V_bus in a high-voltage 50Hz AC system as shown in the figure. The measurement capacitors C₁ and C₂ have tolerances of $$ \pm $$10% on their nominal capacitance values. If the bus voltage V_bus is 100 kV rms, the maximum rms output voltage V_out (in kV), considering the capacitor tolerances, is __________.