# Is there a way to solve this circuit using Nodal Analysis?

Please, take a loot at this circuit: Obviously, this is a circuit that is very easy to solve using lots of different methods. However, I'm trying to solve it using Nodal Analysis (I'm not sure if it's possible).

I tried to use node B as reference. When I do it, I notice that the voltage from C to B is known (10V). The voltage from A to B is already known (20i). So, there's no equation to find.

I would like to know if this circuit is already "solved" (voltages are known) or if I'm missing something here. I just can't find any useful equation taking B as the reference. Even if I try to find a equation using node A, I can't go forward since I can't find find the current that is passing through the dependent source.

Thanks!

• I'm not sure you can say you know the voltage itself from A to B. Yes, you have a current source which sets a voltage, but you don't have the voltage itself. I'd recommend setting up for KCL on the nodes to get the whole system with certainty. May 6 '15 at 3:55
• @Fiire Yes, I agree with you. The point is that I just can't find a way to find the voltage itself using only Nodal Analysis. This is strange, since the point of this method is to find all the voltages related to the reference node. I would expect to get Va as a known number after applying nodal analysis, instead of an equation with an unknown variable i. May 6 '15 at 4:05
• Sorry! I thought the i stood as an indicative for current in ampere. If i is a variable, then yes, the system of equations depends (most probably) on the value of i. May 6 '15 at 4:20

At Node C: (C+20i)/10 + (C+20i)/30 = i

But C=10, hence you can solve for i.

Then, voltage at A is -20i

• Thanks, I didn't realize that a node could be useful even if I already knew its voltage. May 7 '15 at 3:59

You won't be able to set up a traditional Nodal equation for node A because of the dependent voltage source. This brings you down one equation, but in return you get the equation for the dependent voltage source: Va = -20*i ('i' which would also be referenced in your nodal equaton for node C).

So to answer to "can you solve this using nodal analysis" well... I would say yes, but that's assuming that dependent voltage source stuff is somewhat orthogonal.

• So, basically, the only result I get by applying Nodal Analysis in this circuit is the Va = -20i equation? It's kinda strange, since I've solved other circuits using Nodal Analysis and everytime I was able to find exactly the value of each voltage (in this case, Vc and Va). I feel like I didn't successfully applied the method since the results (Vb = 10V and Va = -10i) are still using an unknown variable i. May 6 '15 at 4:02
• That's not including the nodal equation for node C. Although you already know Vc, you can still set up a nodal equation for the currents coming in and out of that node. May 6 '15 at 13:08
• Thanks, I didn't realize that a node could be useful even if I already knew its voltage. May 7 '15 at 3:59