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Power supply is acting like a short but has high resistance


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I'm trying to get a power supply working that I recently have built but have been having constant trouble with it. The most recent problem is that the 3300 uF capacitor discharges instantly as soon as I unplug it from the wall, despite the fact that there is a 1K Ohm resistor and LED in parallel with it and the output reading is currently very low. I have seen the LED slowly get dimmer in the past. I took a resistance reading across the output when the circuit was not energized and it was about 8K and kept rising, I thought it was because the capacitor was charging but after several attempts to discharge it the resistance was still high (17K last I saw.) I have a 5K potentiometer and a 10K resistor in series with the output. I took a reading across the DC rail as well which had high resistance. This thing has me completely stumped.

Also I have been trying to make it a variable power supply and someone said I need to use the potentiometer to control the voltage via a voltage regulator, is there any way to do this with a transistor?

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