DC Distribution System -- Minimum Voltage across the line

[jaus tail]

Homework Statement

Homework Equations

V = IR
And R becomes 2(r of one conductor) because of return path.

The Attempt at a Solution

V minimum is at third junction. At V_D
Using KVL we get:

[/B]
Drop at AB = (10 + 20 + 50) * 2 * 0.1 = 16 V
Drop at BC = (20 + 50) * 2 * 0.08 = 11.2
Drop at CD = (50)*(2 * 0.06) = 6
Total Drop = 33.2 V
V_D = 220 - 33.2 = 186.8V
Why have they not included the 2 factor in their calculation?
In solved examples they have used factor of 2.

Aren't all dc distribution 2 wire as the return path cannot be ground for DC? So shouldn't the factor of 2 be there in the equation?

 

[cnh1995]

So shouldn't the factor of 2 be there in the equation?

No. You should be concerned with only point D here. Out of the four load points, D has the minimum voltage.

 

[jaus tail]

But in solved example they have used factor of 2
Should I use factor of 2 if they say 2-wire dc system and not use factor of 2 if they don't mention 2 wire dc system?

 

[cnh1995]

But in solved example they have used factor of 2
Should I use factor of 2 if they say 2-wire dc system and not use factor of 2 if they don't mention 2 wire dc system?

It is also possible that they have added the return path's resistance in the forward path's resistance (since they are in series) and have replaced the return path with an ideal wire.

Even if you consider the return wire's resistance here, it will not affect the voltages at given points A, B, C and D since the currents of the loads are given.

 

[jaus tail]

The currents are given in solved example also and still they've included the factor of 2. I've marked it red in the picture. Is there some reason when to use 2 and when to not use 2?

 

[cnh1995]

The currents are given in solved example also and still they've included the factor of 2. I've marked it red in the picture. Is there some reason when to use 2 and when to not use 2?

When you have to compute the resistances of individual conductor segments, you need to use the factor of 2 since you need to calculate the resistance of the entire two-wire system first. Here, you have already been given the resistances of the segments of one conductor and you are asked to find the potentials at the tapping points on that conductor. So you need not worry about the return conductor here.

You should consider the voltage drop in the return conducor if they are asking for 'load voltage'. Here, it seems they are asking for 'potential at point D', which is not same as the load voltage at D if you include the resistance of the return conductor.