Resistors in Series and Parallel question

[chunkylumber111]

Hi I have the following question (please see attached). Any help would be much appreciated as I have searched through all the text books I have and couldn't find any similar problems...

 

[ericgibbs]

Hi I have the following question (please see attached). Any help would be much appreciated as I have searched through all the text books I have and couldn't find any similar problems...

hi,
A clue would be that the voltage at the ends of Ze would have to be the same.

 

[Jugurtha]

Another Clue:

What does "zero current" have as an equivalence: "Short Circuit" or "Open Circuit" ?

You can re-draw your schematic with the corresponding equivalence to "see" the solution more clearly.

 

[MrAl]

Hi,

If you have zero current and it's really zero between two nodes than you can open the two nodes and you'll still have zero current.

 

[chunkylumber111]

Thanks for the suggestions, does the direction of the arrows have any significance?

 

[ericgibbs]

Thanks for the suggestions, does the direction of the arrows have any significance?

hi,
The arrows in that diagram are just to indicate the voltage reference points, ie: the bottom line of your circuit is the ref and the two voltages are measured from that ref point.

Have you solved the problem.?

 

[chunkylumber111]

No I'm afraid I still haven't solved it yet! ZE has an open circuit equivalence but should I use node or mesh analysis? And what is meant by the 'condition'? Will the final answer just be Vx = Vy expressed in other terms?...I need help please!

 

[Jugurtha]

ZE has an open circuit equivalence

It's lie it is "unplugged"..

but should I use node or mesh analysis?

Names.. Don't bother with names. When in doubt, follow equations.

Will the final answer just be Vx = Vy expressed in other terms?

This equation is and will be valid for the whole exercise, it is the starting point... What will follow is a consequence of this equation.

So, Vx=Vy means the current in ZE is null. You disconnect it to see more clearly.

Look at the picture I attached.

You are given something, and then tinker with the equations a little bit..

If Vx=Vy , it is then safe to assume that the difference of potential between ZB is equal to that one between ZC.

What does this mean ? Write down the equations in terms of currents. (The currents are I and (I-Ic) )

So, we've got VZA=VZD (1)
VZB=VZC (2)

Write each one in function of the current circulating through each one (example: I-Ic circulates through ZB and ZA so... ? )

You will have two equations on the form X*k=Y*j (1)
W*k=Z*j (2)

The next step to tinker with it would be of course to divide one by the other and get rid of k and j so you only get X/W=Y/Z (And this is equal to (X+Y)/(W+Z) too, we must not forget primary school )

 

[chunkylumber111]

Thanks Jugurtha! so is the final answer: (Zb + Za)/(Zc + Zd) ?

 

[Jugurtha]

Thanks Jugurtha! so is the final answer: (Zb + Za)/(Zc + Zd) ?

When they ask you about the conditions to get a null current through ZE, something like (Zb+Za)/(Zc+Zd) doesn't mean anything .. It's not an equation or something ..

You got asked what are the conditions to get a null current through ZE, you START from this, from what you have been asked and take it as granted, as your starting point, then you "follow" the consequences of a null current through ZE which are:

*ZA and ZB are juiced by the same current.

*ZC and ZD are juiced by the same current.

VY=VZD=VX=VZA

VIN=VX+VZB=VY+VZC , with VX = VY, so they cancel each other we'll have:

VZB=VZC

What does this mean, we write that in currents going through them:

VZB=ZB*(I-Ic)

VZC=ZC*Ic

VZB=VZC ==> ZB(I-Ic)=ZC*Ic .... (1)

VX=VY , written another way ZA(I-Ic)=ZD*Ic ..... (2)


We divide (1) by (2) to get rid of currents to find the CONDITION to have a NULL current on ZE.

So (1)/(2) gives : ZB/ZA=ZC/ZD=(ZB+ZC)/(ZA+ZD) or written in another way, ZB*ZD=ZC*ZA.

That's the condition one the impedances ZA, ZB, ZC and ZD to get a null current on ZE.

So in your circuit, if you chose for example ZB=10 ohms, ZD=2 ohms, ZC=1 ohms, ZA=20 ohms, you'll get a null current on ZE.

Have a look on Wheatstone bridge, but no matter what, in this kind of problems, you are given a constraint, and you kind of "backward" engineer or reverse stuff to get to *satisfy* this constraint.

(In Control Systems for example, you are given desired characteristics of a system (overshoot, damping, pulsation -for a specific sampling time for example-), and you -backward find- its discrete transfer function, and backward find the propper corrector to do that, R-S-T or a special case Pole Placements, etc.. You do the reverse path, you *start from the end* and find the setting to get the desired output)

Good luck,