I'm trying to size a set of resistors for charging a capacitor. The source is a 500V 60Hz AC supply.
The initial instantaneous current is 0.5A sizing the resistors at 125W each. That seems too high because the current decays very rapidly. If the resistors only need charged every 3 minutes or so, how would I size their power requirements?
simulate this circuit – Schematic created using CircuitLab
Best Answer
Well if you were supplying the circuit from a DC supply it would take about 5 time constants before the cap could be regarded as fully charged. You could make the argument that an AC scenario would be no worse because at least the power comes intermittantly over a longer time period giving a little time for the resistor to cool so, stick with the DC circuit is my advice when analysing.
5TCs ia a total elapsed time period of about 17 seconds (on DC) so, you have to start digging around in the data sheets of power resistors to see how much their short term peak overload rating is.
For instance, a 1 watt rated resistor may be able to take 10 watts for 1 second or 100 watts for 0.1 seconds etc.. Regarding the current at any point in the charging process consider this graph: -
Along the base is time (measured in RC time constants). The rising graph tells you the capacitor voltage in terms of percentage fully charged voltage (500 V x 1.4142 and not 500 V).
The falling graph gives you percentage current and at 0.5 CR it is 61% of I max (which happens to be 0.7 A and not 0.5 amps as per the question). So, you could do a calculation based on approximate figures i.e. between t=0 and t=0.5RC you could assume the current to be 100% then, in the next half time constant assume it is 61% etc..
Or, you could do some digging around and develop the exponential formula to give a more precise figure for power.