Node Analysis for Newbies: Solving Current Source Circuits

[James889]

Hai,

I have this simple circuit
[PLAIN]http://img638.imageshack.us/img638/3236/upgp1copy.png

And i simply need to solve for the current delivered by the voltage source Vs.

How do you write the Kvl equations when you have nonlinear elements like the current divider element in this circuit ?

 

[MATLABdude]

Hai,

I have this simple circuit
[PLAIN]http://img638.imageshack.us/img638/3236/upgp1copy.png

And i simply need to solve for the current delivered by the voltage source Vs.

How do you write the Kvl equations when you have nonlinear elements like the current divider element in this circuit ?

HINT: the current in the second loop is given as 1A.
HINT2: What is the value of Vx?
HINT3: What is the nodal equation at the top centre nodal point?

 

[James889]

Hi,

The current over the 18ohm resistance is 18V and 4V for the 4ohm resistor.
Is the current 1A everywhere in the circuit?
And how do you know which way the current flows if there weren't any arrows?

/James

 

[MATLABdude]

Hi,

The current over the 18ohm resistance is 18V and 4V for the 4ohm resistor.
Is the current 1A everywhere in the circuit?
And how do you know which way the current flows if there weren't any arrows?

/James

Correct, however note that the current directions *ARE* identified in this diagram (that's what the big arrow on the dependent supply and the smaller arrow near the 1A are--direction indicators).

The beauty of nodal analysis (and yes, mesh analysis too) is that you can arbitrarily decide that currents will go in a particular direction (you just have to keep these directions consistent). In the end, you'll have a negative sign if the current actually flows in the opposite direction.

You CANNOT assume the 1A is consistent throughout this circuit. That's the whole point of doing this nodal analysis. The current INTO a node must equal the current out. Or, the sum of the currents at a node must equal zero.

Note that the dependent current source Vx/2 is tells you how much current flows through that branch... (Unless Vx/2 is actually a voltage source, and is just drawn incorrectly in the picture you posted).

 

[James889]

Alright, so i have 22V leaving the top node. And I am assuming the algebraic sign for the voltage over the current source is minus.

So the KVL equation for the top node:

22+Vx/2 = 0
Gives Vx = -44

Make sense?

 

[xcvxcvvc]

Alright, so i have 22V leaving the top node. And I am assuming the algebraic sign for the voltage over the current source is minus.

So the KVL equation for the top node:

22+Vx/2 = 0
Gives Vx = -44

Make sense?

nodal analysis uses the sum of the currents entering and leaving the node equaling zero to solve for voltages. You use the sum of voltages around a loop equaling zero to solve for currents in mesh analysis.

 

[MATLABdude]

Alright, so i have 22V leaving the top node. And I am assuming the algebraic sign for the voltage over the current source is minus.

So the KVL equation for the top node:

22+Vx/2 = 0
Gives Vx = -44

Make sense?

in addition to what the post above this one says about summing currents, and not voltages, you ALREADY HAVE Vx, the voltage across the 18 ohm resistor.

To quote my ever-patient junior high school French teacher, "essayez encore!" Try to sum the currents once again, remembering that 1A is exiting on the right.

 

[James889]

So i have a total of 10A in the circuit.
10A over the 2ohm resistor gives V = 20

Total voltage must be 20+18+4 = 42

Embarrassing

 

[xcvxcvvc]

So i have a total of 10A in the circuit.
10A over the 2ohm resistor gives V = 20

Total voltage must be 20+18+4 = 42

Embarrassing

I think you're forgetting that there is a voltage drop across the current source and that the current source can add/remove power from the circuit.