Electrical theory question

MushCreek · June 08, 2013, 04:06:04 PM

I'm doing the calcs for my electrical system, and ran across an interesting problem. I looked up a few standard kitchen ranges to get an idea of power usage, and the way they list the specs doesn't make sense to me. One example listed it as 8.9KW @ 208V, or 11.9KW @ 240V. Huh? Aren't watts watts? Doing some high school math, it works out to 42.8 amps @ 208V, but 49.6 amps @ 240V. Oddly enough, the specs also call for a 40 amp breaker at either voltage. I don't get why the wattage changes so much with the voltage difference, and why a 40 amp breaker is deemed sufficient. It's a 50A outlet anyway, wired on a 50A breaker with wire to suit, but the theory escapes me.

MountainDon · June 08, 2013, 04:33:16 PM

In all likelyhood you do NOT have 208 volts, you have 240. So forget about doing the math.

The 208 volts is a three phase voltage and 220/240 volts is a single phase voltage. Single phase is what residences normally have. If you operate a 220 volt motor on 208 volts the current will be 5% higher that the motor's nameplate rating. If the load is resistive and you operate a 220 volt baseboard heater on 208 volts the true heater wattage will not be reached because of Ohm's law. Current is directly proportional to the applied voltage and inversely proportional to the resistance in the circuit.

June 09, 2013, 05:55:50 AM

That makes more sense. It never occurred to me that they would list an appliance for 3 phase. I've done a lot of 3Ph wiring (more than residential). I'm still curious as to how the math for 240V comes out to nearly 50A, but they call for a 40A breaker. I guess the total wattage is for every element on at the same time, something which is unlikely, or maybe not even possible.

NM_Shooter · June 10, 2013, 02:40:50 PM

Light bulbs and heaters are primarily a resistive load. Not much inductance, as compared to AC motors.

If you calculate the hot resistance of the element (cold resistance is much, much lower) you get the following:

Using R= (V^2) / P

For 208V and 8900W, element resistance is 4.86 Ohms.

For 240V and 11900W, element resistance is 4.84 Ohms.

You would expect the 240V rating to have a lower resistance, and it actually does, but the numbers look funny mostly because of significant digits and rounding. If we measured more carefully this would become apparent.

For example, measure a 100W light bulb with Ohm meter. Mine measures 10.1 Ohms. Calculating the power of a 10.1 Ohm load with 120V across it yields a power consumption of 1400+ Watts. But as the bulb element, or the stove element heats up, the resistance also goes up... a lot. That initial inrush current is huge. Until the element heats up, it is sucking a lot of current. This is also why bulbs tend to pop when you first turn them on. Using a dimmer circuit to more gently apply power to the bulb improves its life.

Anyway.... Back to your stove. I am suspicious about the 40Amp breaker rating for your stove, seeing as the max load for your stove will be much more than that. I think that the reason is probably that a lot of older houses have 10ga wire that was run for the oven, long before folks were putting in 12kW appliances 

The safe way to do this is to determine the gauge of your wire, and base your breaker capacity off of the wire gauge, and NOT the rating on the oven.

Good luck!

MushCreek · June 10, 2013, 06:02:58 PM

It's the manufacturer that lists the 40A rating. Almost all of the ranges I looked up were the same. I'm running 6/3 wire on a 50A breaker to a 50A outlet, so I know I'm covered.

June 10, 2013, 06:44:11 PM

The manufacturer is covering their butt...The range is rated at the full capacity of all burners going, but they probably don't consider you are going to run every burner in the thing at the full load.

Many of the manufacturers also derate for variations in line level too.

Can I guess at the manufacturer of that stove? Is it GE? What model number? I called them once for a somewhat similar tech question and they simply were unable to answer.

Take a look at the manufacturer spec sheet that is online. Add up all the burner wattage. I speculate that the total you come up with is less than the advertised 11.9kW.

flyingvan · June 10, 2013, 07:54:06 PM

The 40a breaker---Since it's 240v, it'll be a double gang breaker, isn't it 40 amps on each 120 leg?

NM_Shooter · June 10, 2013, 08:29:14 PM

Yes, but it is not cumulative. So if either leg exceeds 40A, it trips. 40A each at 120, is not 80A at 240. Still only 40A limit. The leg can fail to the other leg, or fail to ground, and it will trip at 40. Sort of. 41A load on a 40A breaker will take a long time to trip.

flyingvan · June 10, 2013, 11:39:19 PM

Hmm...I'm getting somewhere around 25 amps on each leg...40 would trip either leg, as you say, but since the two legs are in different phases the breaker on either leg doesn't see the cumulative amperage..At least that's how I understand it. I'm very open to being re-educated and have much experience at being wrong

June 11, 2013, 08:23:19 PM

Quote from: MushCreek on June 09, 2013, 05:55:50 AM
That makes more sense. It never occurred to me that they would list an appliance for 3 phase. I've done a lot of 3Ph wiring (more than residential). I'm still curious as to how the math for 240V comes out to nearly 50A, but they call for a 40A breaker. I guess the total wattage is for every element on at the same time, something which is unlikely, or maybe not even possible.

I have a friend that does new construction, NEC permits #8 wire on a 40 breaker for a range circuit. I found

Quote from: flyingvan on June 10, 2013, 11:39:19 PM
Hmm...I'm getting somewhere around 25 amps on each leg...

I've never seen more than 30 amps on a clamp ammeter with every burner on maximum. Sounds typical to me

MushCreek · June 13, 2013, 06:11:11 AM

Interestingly, my very ordinary small ranch home in a subdivision has a 50A circuit for the range. I already have the breaker and the cable, so I'm putting in 50A as well.

flyingvan · June 13, 2013, 09:09:30 AM

I'd stick with the recommended size breaker for the appliance----the goal isn't to keep a breaker from tripping, but to have it trip as soon as there's a problem. Fairly common point of origin for fire investigation----investigators go to the panel and see an oversized breaker. If it's oversized for the appliance the fire starts at the appliance. If it's oversized for the wiring, it starts in the wall somewhere.

Rob_O · June 13, 2013, 06:28:23 PM

Quote from: MushCreek on June 13, 2013, 06:11:11 AM
Interestingly, my very ordinary small ranch home in a subdivision has a 50A circuit for the range.

As it should, the change was fairly recent

MushCreek · June 14, 2013, 05:15:50 AM

Quote from: flyingvan on June 13, 2013, 09:09:30 AM
I'd stick with the recommended size breaker for the appliance----the goal isn't to keep a breaker from tripping, but to have it trip as soon as there's a problem. Fairly common point of origin for fire investigation----investigators go to the panel and see an oversized breaker. If it's oversized for the appliance the fire starts at the appliance. If it's oversized for the wiring, it starts in the wall somewhere.

Good point- maybe I need to re-think the 50A breaker. No harm in using the heavier wire, though. The mini-split A/C I'm planning to use calls for a 15A breaker, but no larger than a 20A. Now I see why.