# Ideal Voltage/Current Source Circuit Analysis

I am trying to understand what it going on in this circuit diagram and how to go about solving this problem. I am told to find Vx given that the current in the central wire is zero. Does this mean that I can interpret the circuit as if the center wire (in which the current is zero) isn't there?

I think that I am still confused about how ideal current sources behave in circuits -- how to calculate voltage across them, whether they have resistance and how to calculate it if they do.

Currently, the only way I think I can think of solving this problem is by interpreting the diagram as if the center wire is not there, and then finding Vx such that 4mA passes through the 1k, 5k, and current source in series.

Any help would be greatly appreciated!

-Matt

• Yes, a wire with zero current through it behaves the same as no wire, so you can delete the wire as it will make the problem much easier to solve. Commented Jan 30, 2018 at 5:01
• Probably the easiest thing to do is to realize that there cannot be a voltage difference if there is no current through the "jumper wire." So, break the connection and call the (-) terminal of $V_X$ as "ground." Clearly, the node between the $1\:\text{k}\Omega$ and $5\:\text{k}\Omega$ resistors must also be a "virtual ground," then. There is only one possible voltage value for $V_X$, given that there is $4\:\text{mA}$ in it and the $1\:\text{k}\Omega$ resistor (with their other ends at "ground.")
– jonk
Commented Jan 30, 2018 at 5:25

It's probably conceptually easier to keep the wire there, and treat the total current as the sum of two currents in the wire.

If you look at the right hand loop, you know that the 4mA source is forcing 4mA through the wire. You don't have to work out what its voltage is, or anything around the 5k resistor. Just the fact that it's a current source means that 4mA will flow.

That means you can solve the left hand loop by itself. What Vx, given that you are given the value of 1k for the resistor, will force 4mA through the wire, in a direction to cancel out the current source's 4mA, to give a total of zero?

• If I only look at the left hand loop, using Ohm's law I calculated that the voltage Vx must be -4.0 Volts, which will generate of current of -4 mA. This makes sense if I interpret the current source as an open circuit and assume that the current only goes to cancel out the +4 mA from the current source and not into the middle wire. Commented Feb 3, 2018 at 21:50

Maybe it is helpful to you to interpret the 0 mA wire as a wire with another current source in it which drives 0 mA. In that case your problem is reduced to a problem of a linear network with just some independent sources in it.

To solve this, as you may already know, you just consider one source at once. To do this, all other voltage sources got replaced by shorts and all other current sources by open circuits. So, for example, if you want to calculate the impact of Vx, you just have to replace both the 4 mA source as well as the fictional 0 mA source with open circuits. Then you can calculate currents and voltages as normal. For the current sources you have to replace Vx by a short circuit and the other current source with an open circuit. After calculating all the currents and voltages for all the three sources independently you just sum up voltages / currents that belong together, e.g. all the voltage drops across our fictional 0 mA current source. That will result in the actual solutions for voltages / currents.