# Resistor Power Capacity

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#### JMB

I am looking to see if there is a formula (not just a rule of thumb) that might predict a resistor's capacity to handle a rapid high voltage pulse. I am designing a capacitor discharge tool and attempting to understand the mathematics behind how a 25 watt resistor might handle much more power for a brief pulse. I understand that it has to do with the thermal build up, etc. I am looking to see if there is some sort of relationship between time and power that would identify a relative power handling ability of the resistor for that time.

Thanks,
Jay

#### JMB

Thanks, Sreten. I was really looking for formula explanations; I will attempt to derive them from the graphs. I was thinking along the lines of 50,000 Volts, 1M Resistor, and .002 MicroFaradays and attempting to establish the wattage capacity requirement of the resistor. I am aware of Sam Goldwater's site and this recommendation - just attempting to figure out how they arrived at the recommendation of 10 Watt Resistor.

Thanks, again.

#### Mooly

Paid Member
Hi, Can't really help with a formula as it is the manufacturers voltage rating that is important. All resistors have a maximum voltage rating to be observed, even if power dissipation is negligable. Have a look at some old "CRT" TV spares, some old (really old) T.V.s had a resistor directly across the EHT supply (25KV rating) to help with regulation and smoothing in combination with the CRT,s Aquadag coating. Old focus controls similar. Microwave oven spares perhaps ?
Regards Karl

#### h_a

Well, it shouldn't be too hard to calculate this.

Assume that below a critical voltage (max voltage of the resistor) the power dissipation is only limited by case temperature (given in the datasheet). Calculate simply the stored energy in the cap and then the resulting power given the esr value of the cap. This gives you a simple differential equation for power as function of time.

behind how a 25 watt resistor might handle much more power for a brief pulse.

It's not power, it's energy. Power is energy per second and that is limited. As long as no other factors limit, the energy at a certain fraction of 1s can be as high as you like, provided the integrated energy (integration over 1s) stays the same.

This is just the mathematical side of things, I'm in no way involved with your special topic, so please get also additional advice from people working in this field.

All the best, Hannes

#### sreten

JMB said:
Thanks, Sreten. I was really looking for formula explanations; I will attempt to derive them from the graphs. I was thinking along the lines of 50,000 Volts, 1M Resistor, and .002 MicroFaradays and attempting to establish the wattage capacity requirement of the resistor. I am aware of Sam Goldwater's site and this recommendation - just attempting to figure out how they arrived at the recommendation of 10 Watt Resistor.

Thanks, again.

Hi,

Energy stored in a capacitor = 0.5CV*V = 2.5J
2.5J = 2.5 watts for 1 second.
Peak power = V*V/R = 2.5kW, peak current = V/R = 50mA.
Time constant = RC = 2ms = time to drop to 37% of full V,
Capacitor mostly discharged, 99% after 5 times RC.

I do not think you can arrive at 10W continuous rating by formala.

/sreten.

#### peranders

Paid Member
JMB said:
I am looking to see if there is a formula (not just a rule of thumb) that might predict a resistor's capacity to handle a rapid high voltage pulse.
Good question but this is very dependent of the ressistor type but in general wirewounded resistors can handle more than film dito.

If you are up to high voltage you must use high voltage resistors. Caddock has lot's of these.

#### unclejed613

a company i worked for had 8ohm 3W resistors on a banana piug for discharging caps. these were carbon comp resistors and would get hot while discharging 20000uf caps (this was on a production line) charged to 65V, but not burn out. our parts department began ordering metal film resistors that externally looked like the carbon comp resistors. i discovered this after losing my discharger and making a new one. i discharged a cap (or thought i did) and then proceeded to get "bit" by the cap. "WHAT?, i just discharged this cap...." the discharger had gone open. i tried other resistors and found they went open as soon as i tried to discharge the cap. the new metal film resistors didnt work well as dischargers, they burned open almost immediately.

btw Mr moderator, can you tell me why certain punctuation such as slashes and apostrophes are being interpreted as control codes while i type this reply?

#### h_a

A nice and elegant estimate sreten!!

Have fun, Hannes

#### JMB

Thanks, guys. I have made a good number of attempts using lots of formlae (including those listed by Sreten) and fudge factors and nothing clearly predicted the numbers seen under the article I sited. I guess that there is a certain amount of gestalt involved in predicting this.

Thanks,
Jay

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