Transformer Problem

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ed downey

Senior Member
Location
Missouri
I would like a second opinion on the attached problem.

I calculate the first part as follows:
I1 = 100W/120V = 0.833A
I2 = 100W/120V = 0.833A
I3 = 0A
IA = I1 + I3 = 0.833A + 0A = 0.833A
IB = I2 + I3 = 0.833A + 0A = 0.833A
IN = IA - IB = 0.833A - 0.833A = 0A
Therefore Since IA = IB There will be no current on the neutral

2nd Part:
I1 = 200W/120V = 1.667A
I2 = 60W/120V = 0.5A
I3 = 0A
IA = I1 + I3 = 1.667A + 0A = 1.667A
IB = I2 + I3 = 0.5A + 0A = 0.5A
IN = IA - IB = 1.667A - 0.5A = 1.167A

Therefore there will be 1.167A flowing to ground.

Can someone please take a look at this I think it is correct but something doesn't feel right.

Thanks,
Ed
 

winnie

Senior Member
Location
Springfield, MA, USA
Occupation
Electric motor research
Your numbers are for calculating your neutral current.

I am concerned about your statement about 1.167A flowing 'into ground'. Why would any current at all flow 'into ground'?

-Jon
 

don_resqcapt19

Moderator
Staff member
Location
Illinois
Occupation
retired electrician
I think that the question is really looking for the voltages across the loads with an open neutral. In the first case with equal loads the two loads will be in series and half of the total voltage will be dropped across each load. In the second case the loads are not equal and the most voltage will be dropped across the load with the highest resistance, in this case the 60 watt lamp. For all practical purposes the resistance of the loads is indirectly proportional to the wattage. The total wattage is 260 and the 200 watt load has 76.9% of the wattage and 23.1% of the resistance. The 60 watt has 23.1% of the wattage and 76.9% of the resistance. 76.9% of the total voltage or 184.6 volts will be dropped across the 60 watt load and 55.4 volts will be dropped across the 200 watt load.
There is no path to earth and in neither case will any of the current or voltage flow from the open neutral to the earth.
 

ed downey

Senior Member
Location
Missouri
Don,

Thanks for the response.

A couple of questions though.

1.) If the neutral conductor is broken at the transformer (between the transformer and the grounding point) but yet you still have a ground reference point since the conductor is grounded and you have an unbalanced load as in the second part of the question. Will the unbalanced part of the current (Which used to flow on the neutral back to the source) now flow on the grounding conductor through the earth and back to the source?

2.) since a neutral conductor is a reference point and it is broken at the transformer yet you still have a grounding connection won't it act the same as a neutral?

Thanks for any help
-Ed
 

don_resqcapt19

Moderator
Staff member
Location
Illinois
Occupation
retired electrician
ed downey said:
Don,

Thanks for the response.

A couple of questions though.

1.) If the neutral conductor is broken at the transformer (between the transformer and the grounding point) but yet you still have a ground reference point since the conductor is grounded and you have an unbalanced load as in the second part of the question. Will the unbalanced part of the current (Which used to flow on the neutral back to the source) now flow on the grounding conductor through the earth and back to the source?

2.) since a neutral conductor is a reference point and it is broken at the transformer yet you still have a grounding connection won't it act the same as a neutral?

Thanks for any help
-Ed
Ed,
With the neutral open between the transformer and the grounding electrode, the system is an ungrounded system. There is no path from the grounding electrode back to the transformer and no current will flow. Current can only travel back to its source...it does not try to get to earth.
 

scott thompson

Senior Member
Reply to the OP

Reply to the OP

Here are the numbers to explain what will happen in both Scenarios...
(to keep things simple, we will use a 1 Phase center tapped Transformer for these examples - such as used in most Residential areas)

BTW, symbols are:

  • "E" = Voltage,
  • "I" = Amperes,
  • "R" = Resistance (across a fixed Resistance),
  • "P" = True Power (Watts).

................................................................................

* Scenario #1:
Two (2) 100 Watt, 120V Incandescent Lamps are used,

* Scenario #2:
One (1) 60 Watt 120V Incandescent Lamp + One (1) 200 Watt 120V Incandescent Lamp are used.

***SCENARIO #1***

Breaking the Common Neutral's connection between the Lamps' Circuit and the Transformer will result in both Lamps operating properly, without one - or both of the Lamps failing.

Description:

100 Watt, 120V Lamp (Incandescent) Data:

P = 100 Watts,
E = 120 VAC,
I = 0.8334 Amps (rounded up),
R = 143.9884 Ohms (rounded up).

If the Circuit is connected normal (no open neutral), the values across each Lamp will be:
E = 120V,
I= 0.8334 Amps.

The total Resistance per circuit (L-N) will be 143.9884 Ohms on "Each Side"
(Line 1 to N = 143.9884 Ohms, Line 2 to N = 143.9884 Ohms).

Each Lamp will have 0.8334 Amps pushed across the Filament by 120 VAC, with a resulting Power drawn of 100 Watts.

If the Common Neutral is opened between the Transformer and the Lamps' circuit (Open Neutral), the circuit values will now be:

Total Circuit E = 240 VAC,
Total Circuit R = 287.9768 Ohms

E ? R = 0.8334 Amps

Total Circuit I = 0.8334 Amps

Per-Lamp:

With 0.8334 Amps flowing through a fixed Resistance of 143.9884 Ohms, the resulting Voltage (potential difference) across the filament of each Lamp is 120 VAC:

R ? I = E
143.9884 ? 0.8334 = 120 Volts

As with the first example (normal circuit) each Lamp will have 0.8334 Amps pushed across the Filament by 120 VAC, with a resulting Power drawn of 100 Watts:

E ? I = P

120 ? 0.8334 = 100 Watts

100 Watts is the Lamp's rating, so the Lamp does not become damaged from excessive True Power draw.

***SCENARIO #2***

Lamp values:

* 60 Watt Incandescent Lamp:

E = 120 VAC,
P = 60 Watts,
I = 0.5 Amps,
R = 240 Ohms.

* 200 Watt Incandescent Lamp:

E = 120 VAC,
P = 200 Watts,
I = 1.667 Amps (rounded),
R = 76.85 Ohms (rounded)

In a "Normal" 3 Wire Circuit, each Lamp's filament has a Potential Difference of 120 VAC across it.

The 60 Watt Lamp allows 0.5 Amp to flow across it, and the 200 Watt Lamp allows 1.667 Amps to flow across it.

The common neutral will have 1.17 Amps flowing between the Lamp circuit and the Transformer.

Each Lamp will draw the rated True power (Watts) from the source, and therefore will operate properly without damage from excessive Power drawn through the filament.

If the Common Neutral of this 3 wire circuit is broken between the Transformer and the Lamps' circuit, the following will result:

* Total Circuit Voltage = 240 VAC,
* Total Circuit Resistance = 311.85 Ohms,
* Total Circuit Amperes = 0.7696 Amps,
* Total Circuit True Power = 184.7 Watts.

The 60 Watt Lamp will have the following values across its filament:
R = 240 Ohms,
E = 184.7 Volts,
I = 0.7696 Amps,
P = 142.15 Watts.

The 200 Watt Lamp will have the following values across its filament:
R = 71.85 Ohms,
E = 55.3 Volts,
I = 0.7696 Amps,
P = 42.56 Watts.

The 60 Watt Lamp will fail rapidly, due to the excessive True Power drawn from the supply, and "Dumped" into the Lamp's filament.

The True Power (Wattage) has exceeded the Lamp's rating by >300%.

The 200 Watt Lamp will be very dim, since the True Power drawn from the supply and 'Dumped" into the filament will only be 42.56 Watts.

The above Scenarios are the reasons why Equipment / Loads fry when higher than rated Voltage is applied to them.

Scott
 

ed downey

Senior Member
Location
Missouri
Scott,

Thanks for the reply.

I am having a little trouble understanding the following scenario.

If you lift the neutral but still have a grounding conductor between the 1st lamp and the second lamp. isn't the potential between the Line A and ground 120V and the potential between Line B and Ground 120V?

See attached circuit drawing.

I am having a hard time understanding this.

Thanks,

Ed
 

winnie

Senior Member
Location
Springfield, MA, USA
Occupation
Electric motor research
Ed,

I believe that the 'concept of ground' is what is confusing you. 'Ground' is not a perfect current sink, nor is it a perfect voltage reference for all points in a system. Ground is simply a conductor, and a poor one at that. The only thing that ground has going for it is that there is so darn much of it.

The only thing that sets the potential between the line conductors and 'ground' is the voltage on the various circuit elements that are actually connected to the ground. In a normal residential service, you have a center tapped transformer where the center tap is directly connected to a grounding electrode. This connection forces the transformer terminals to be at a well defined voltage relative to that grounding electrode. Without that grounding electrode connection, the relationship between the line conductors and ground becomes undefined. You could just as easily connect one of the line terminals to that grounding electrode, and it would be forced to zero volts relative to ground; the transformer neutral would be at 120V relative to ground, and the 'far' line would be at 240V relative to ground.

In the circuit that you drew, you have only one connection to 'ground'. That connection is what will define the line to ground voltages. Because that connection is via an unbalanced load, the line to ground voltages will be forced to be unbalanced.

Now, if your transformer neutral were connected to a grounding electrode, and your circuit neutral were connected to a grounding electrode, then you would have a slightly different story. As noted above, ground is simply a conductor, so if there is any voltage difference between the two grounding electrodes, current will flow between them. Also as noted above, ground is a _poor_ conductor, so the amount of current flow will not be very much. If you had the two grounding electrodes, what you would find is that the 'line to soil near the transformer ground electrode' would be 120V, and the 'line to soil near the neutral ground electrode' would be something other than 120V, with a fraction of an amp flowing between the two electrodes.

It is known that you can take a 120V 'hot' and run it to an isolated ground rod in soil. You will get a few amps flowing into the ground rod, and you may electrocute some worms (or yourself)...but the circuit breaker won't trip, and the current flow won't be particularly high.

-Jon
 

don_resqcapt19

Moderator
Staff member
Location
Illinois
Occupation
retired electrician
Scott,
All of that math to get the same answer that I got just using the percentage of total wattage:grin:
 

ed downey

Senior Member
Location
Missouri
I think I may be a little hard headed but I now understand the point that Don, Scott, & Jon are saying. Thanks for the additional information.

I may be a little slow but once I get it doesn't get away:grin:

-Ed
 
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