[Circuits] Solving a KCL Problem

[ainster31]

Homework Statement

Homework Equations

The Attempt at a Solution

Here is what I don't understand: how can this circuit exist? If you look at the V2 node, there are 3 currents going in but none going out. Isn't this a contradiction? From what I've heard, you can arbitrarily draw current arrows and if the direction of the arrows is wrong, you'll just get a negative current. But don't you have to at least be consistent in the rotation? If you look at the bottom left mesh, the currents are going clockwise and then there is a current that is going counter-clockwise.

 

[gneill]

Here is what I don't understand: how can this circuit exist? If you look at the V2 node, there are 3 currents going in but none going out. Isn't this a contradiction? From what I've heard, you can arbitrarily draw current arrows and if the direction of the arrows is wrong, you'll just get a negative current. But don't you have to at least be consistent in the rotation? If you look at the bottom left mesh, the currents are going clockwise and then there is a current that is going counter-clockwise.

So long as you're consistent in writing the math according to your assumed currents, the math will always take care of itself and present you with the right values (positive or negative) for each.

In fact, when writing node equations it's actually easier to maintain consistency by always assuming that all currents are flowing either into or out of a given node. That way you never trip up by forgetting which one or ones you had going in and which ones going out. Later, if you need the value of a particular current, you use solved-for node voltages and Ohm's law for a given branch.

 

[Tanya Sharma]

Here is what I don't understand: how can this circuit exist? If you look at the V2 node, there are 3 currents going in but none going out. Isn't this a contradiction?

No...there isn't any contradiction .The confusion clears as soon as you calculate V₂ ,which you haven't .V₂ = 62.89 V which means it is higher than both 60V and V₁ .So,in reality a current of magnitude 0.29A flows from V₂ to 60V across the 10Ω resistor and 4.90A from V₂ to V₁ across 2Ω resistor .

In other words at node V₂ ,current of magnitude 5.19A enters whereas 0.29A and 4.90A leave .

It is your assumption that all currents are flowing into node V₂.But in reality that is not the case .

Hope that helps