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The two circuits are totaly different. In the first you have a time contant of 62 seconds. (10 uF and 6.2 Meg.) In the second you have a time constant of 3.4 seconds (10 uf and about 340K. The 340K is the 6.2M in parallel with the 360K) even worse in the first circuit you charge the capacitor via the 1K and then you open the switch. In the second circuit you charge the capacitor while the input pulse is high but when it goes low the capacitor is being dischaged through the 1 K resistor. You could get round yhis by adding a diode between the input pulse and the capacitor . (+ end to the capacitor.)