Dazed and confused..

Hi, I'm having trouble understanding this problem.

The voltage Va for the network below is -1 V. If it suddenly jumped to 20 V, what could have happened to the circuit structure?

Since the chapter introduces short and open circuits, I'm assuming it has something to do with that but I don't really understand the drawing. Is this supposed to be a branch of some larger network with some unknowns that I have to determine first?

No, you do not need to determine any unknown.
You need to think what could have happened to 4K and 3K resistors to get Va equal 20V

Label the resistors Ra, Rb, And Rc. What happens to the voltage at point a when any one of them changes? Do you know how a voltage divider works? That the voltage sources will cause currents in the resistors, and that those currents can be calculated to find the voltage dropped over each resistor?

beenthere said:

Label the resistors Ra, Rb, And Rc. What happens to the voltage at point a when any one of them changes? Do you know how a voltage divider works? That the voltage sources will cause currents in the resistors, and that those currents can be calculated to find the voltage dropped over each resistor?

Click to expand...

Ok, how is this?

Total voltage=20 V - 4 V=16 V

Current=16 V/(4+3+1)kΩ=2mA

U1=2mA*4kΩ=8 V

U2=2mA*3kΩ=6 V

U3=2mA*1kΩ=2 V

TwoPlusTwo said:

Ok, how is this?

Total voltage=20 V - 4 V=16 V

Current=16 V/(4+3+1)kΩ=2mA

U1=2mA*4kΩ=8 V

U2=2mA*3kΩ=6 V

U3=2mA*1kΩ=2 V

Click to expand...

Wrong
Total voltage is equal
20V - (-4V) = 24V

TwoPlusTwo said:

Total voltage=20 V + 4 V=24 V

Current=24 V/(4+3+1)kΩ=3mA

U1=3mA*4kΩ=12 V

U2=3mA*3kΩ=9 V

U3=3mA*1kΩ=3 V

Click to expand...

Ok. I fixed it. So is the rest of it ok?

And why exactly is Va = - 1 V?

Yes, looks ok

I still don't understand why Va has to be -1 V in this configuration. But if I were to guess at a solution to the original problem it would be that Va has jumped from -1 V to 20 V because the 4k and 3k resistors have been shorted out. Does that make sense?

TwoPlusTwo said:

I still don't understand why Va has to be -1 V in this configuration.

Click to expand...

Becaues Va voltage in not a voltage drop across 1K resistor.
Va is a voltage between Va and GND.

TwoPlusTwo said:

But if I were to guess at a solution to the original
problem it would be that Va has jumped from -1 V to 20 V because the 4k and 3k resistors have been shorted out. Does that make sense?

Click to expand...

Yes, you right

Great! I think I understand. Va is given by

- 4 V + U3 = - 4 + 3 V = - 1 V

Great job

Overly thought out problem. What caused the voltage drops? What if the current somehow became zero (series circuit)

Jony130 said:

No, you do not need to determine any unknown.
You need to think what could have happened to 4K and 3K resistors to get Va equal 20V

Click to expand...

You also need to consider a fault in the 1k resistor.

Twoplustwo dont let the change of schematics throw you off. Think of this as a branch of huge circuit that you are inspecting in a lab. You have a branch that has these resistor in series and the voltages you have (20v,-1v,-4v) you have attained using a voltmeter.
the voltage drop over (4k+3k) is simply 20-(-1) =21v =>21v/(7k)=3mA
the voltage drop over (4k+3k+1k) is simply 20-(-4)=24v=>24v/8k=3mA