Solving for current between 2 nodes

[grekin]

Homework Statement

Assume that I = 22mA , V = 6.0V , and R = 350Ω. Determine the current between B and D using the superposition principle.

Homework Equations

V=IR
Superposition Principle
G=1/R
Voltage and Current dividers
KCL, KVL

The Attempt at a Solution

I_BD = I_BD' + I_BD''

Shorting the voltage source first, I have:

R_eq of resistors now in parallel = 100*300/(100+300) = 75

Applying the current divider to the remaining circuit, I have:

I_BD'' = -0.022 * 300/825 = -0.008

(I also solved this using mesh analysis and got the same answer)

Now replacing the current source with an open circuit, I have:

R_eq from A to C to D to B = 750

Combining that with the 300 Ohm resistor it is now in parallel with, then with the 100 Ohm resistor in series, I have:

R_eq = 314.3

Solving for total current with V=IR, I_total = 0.019 A

Applying the current divider:

I_BD' = 0.019*300/1050 = 0.0054 A

Combining I_BD' and I_BD'', I_BD = -0.0026 A which is incorrect. Not exactly sure what I'm doing wrong here.

 

[gneill]

Presumably the current I_BD is meant to refer to the current from B to D. If so, check the assumptions you're making about the direction of current flow for each case.

 

[grekin]

I think I see my mistake, but I just want to be sure before putting in an answer because I'm on my last attempt. I believe I mixed up the sign with the current source removed, so it should be -0.0054 A and the total I_BD should be -0.0134. Does this sound correct?

 

[gneill]

I think I see my mistake, but I just want to be sure before putting in an answer because I'm on my last attempt. I believe I mixed up the sign with the current source removed, so it should be -0.0054 A and the total I_BD should be -0.0134. Does this sound correct?

Your new current for when the current source is suppressed looks good. But also check the sign for the case where the voltage supply is suppressed. What direction will the current BD flow then?

 

[grekin]

Your new current for when the current source is suppressed looks good. But also check the sign for the case where the voltage supply is suppressed. What direction will the current BD flow then?

So I guess both my signs were mixed up then, which sounds right but my problem with that is it gives me 0.0026 A for I_BD, which I had put in earlier and it said I was wrong.

 

[gneill]

So I guess both my signs were mixed up then, which sounds right but my problem with that is it gives me 0.0026 A for I_BD, which I had put in earlier and it said I was wrong.

So you've got:
When I source is suppressed: -5.45 mA
When V source is suppressed: 8.00 mA

making the sum I_BD = 2.54 mA

Your system may require that your answer have a certain number of significant digits and particular units. How exactly do they want the input to be given?

 

[grekin]

It specifically asks for 2 significant figures. I could try 0.0025 A but I'm not sure if it'll make a difference, usually it accepts the answer if you're only a tad off.

I'll probably end up talking to my professor about it tomorrow, because this seems like the correct answer.

EDIT: I took the risk and put in 0.0025 A, which is indeed correct. Thanks for your help.

 

[gneill]

Well, 0.0026 is not the quite the same thing as 0.0025. 2.54 mA doesn't round to 2.6 mA.