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In the third example, at t=0, isn't the source short circuited? Capacitors don't have initial voltage so at t=0+, both capacitors are short circuited and so as the resistor and that makes the source shorted.. isn't it?
No. Actually, in this example Capacitor doesn't follow its property of holding charge. At t=0-, it has 0V but at t=0+, it will have Vi/2 voltage. Why so? (I have explained in the video) that whenever there is a condition of infinitely large current in a ckt, capacitor and inductor Don't follow their own property.
Also, the step input at t=0+ can be taken as sinusoid of infinite frequency (I have explained this concept in further videos) so because of high frequency, Parallel combination of Resistor and Capacitor can be replaced simply by the capacitor (as it has lower impedance at high frequency) and now simply you can divide the voltage as per the capacitance value.
