In the circuit shown below, the supply voltage is 10sin(1000t) volts. The peak value of the steady state current through the 1Ω resistor, in amperes, is _________.

The circuit below is excited by a sinusoidal source. The value of R, in Ω, for which the admittance of the circuit becomes a pure conductance at all frequencies is ________.

A symmetrical square wave of 50% duty cycle has amplitude of ±15V and time period of 0.4$$\mathrm\pi$$ ms. This square wave is applied across a series RLC circuit with R = 5Ω, L = 10 mH, and C = 4μF. The amplitude of the 5000 rad/s component of the capacitor voltage (in Volt) is __________.

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 ________.