I need help setting the nodal equation up for this problem.
- Thread starter Braiden
- Start date
A few things you need to clean up before we can proceed. Your schematic has to DC voltage sources, 12 V and 9 V, but the symbol you are using is non-standard and symmetric, which means that there is no way to tell what the polarities of these two sources are. So that needs to be fixed. The standard symbol for a battery is a stack of symbols for a cell and the symbol for a cell is a wide line and a narrow line with the narrow line being the negative side of the cell. Another option is to just put a '+' symbol by the positive terminal of the battery.
Then in the big clear space in the middle you have V1 - 750 mA. I don't know what you are trying to convey with this expression, but note that you cannot subtract a current from a voltage. In order to add or subtract two quantities, the units must be the same.
You should get in the habit of carrying your units throughout your work -- you will catch many of the mistakes you make right when you make them by doing so.
In the equation you setting up in the bottom half of the paper, you have (Va - 9V)/1 kΩ twice.
Is (Va - 9V) the voltage appearing across either one of those resistors?
Even if you had the proper voltages across those two resistors, do those two currents sum together as they flow into Node A?
So patch things up as best you can based on this and we'll see where that leads.
Then in the big clear space in the middle you have V1 - 750 mA. I don't know what you are trying to convey with this expression, but note that you cannot subtract a current from a voltage. In order to add or subtract two quantities, the units must be the same.
You should get in the habit of carrying your units throughout your work -- you will catch many of the mistakes you make right when you make them by doing so.
In the equation you setting up in the bottom half of the paper, you have (Va - 9V)/1 kΩ twice.
Is (Va - 9V) the voltage appearing across either one of those resistors?
Even if you had the proper voltages across those two resistors, do those two currents sum together as they flow into Node A?
So patch things up as best you can based on this and we'll see where that leads.
(Note: They don't necessarily teach this stuff)
Before writing the node equations one needs to prepare the circuit diagram for nodal analysis:
1 - Identify the reference node (if not already done for you).
2 - Color-code the nodes and supernodes.
3 - Label the node voltages.
N/A 4 - Label the supernode voltage offsets.
N/A 5 - If there are dependent sources, express the control variable in terms of the node voltages.
N/A 6 - Mark the control variable expressions on the circuit diagram.
7 - Write a node equation for each node or supernode; except the reference node or ground-supernode. All the information necessary to write a node equation will be clearly displayed on the circuit diagram.
There is more than one way to form the node equations, but the most important consideration is to do it exactly the same way every time. Being consistent will remove any uncertainty about the result. Nodal analysis is a procedure, so follow the procedure. The great object is to substitute consistent procedure for making assumptions on the fly which may be different for every problem. Making assumptions is just another opportunity for making errors. Note that understanding what the circuit is doing is optional because correctly following the procedure will yield equations that describe what the circuit is doing. Suggested procedure: Every term in the node equation begins with the voltage of that node, so each term has the form (Node Voltage - Adjacent Node Voltage)/(Resistance to Adjacent Node). One consequence of using this form is that current leaving the node is considered positive, so this determines the sign of any current sources attached to the node. For each node equation, sum all the pathways to adjacent nodes and set it equal to zero.
Before writing the node equations one needs to prepare the circuit diagram for nodal analysis:
1 - Identify the reference node (if not already done for you).
2 - Color-code the nodes and supernodes.
3 - Label the node voltages.
N/A 4 - Label the supernode voltage offsets.
N/A 5 - If there are dependent sources, express the control variable in terms of the node voltages.
N/A 6 - Mark the control variable expressions on the circuit diagram.
7 - Write a node equation for each node or supernode; except the reference node or ground-supernode. All the information necessary to write a node equation will be clearly displayed on the circuit diagram.
There is more than one way to form the node equations, but the most important consideration is to do it exactly the same way every time. Being consistent will remove any uncertainty about the result. Nodal analysis is a procedure, so follow the procedure. The great object is to substitute consistent procedure for making assumptions on the fly which may be different for every problem. Making assumptions is just another opportunity for making errors. Note that understanding what the circuit is doing is optional because correctly following the procedure will yield equations that describe what the circuit is doing. Suggested procedure: Every term in the node equation begins with the voltage of that node, so each term has the form (Node Voltage - Adjacent Node Voltage)/(Resistance to Adjacent Node). One consequence of using this form is that current leaving the node is considered positive, so this determines the sign of any current sources attached to the node. For each node equation, sum all the pathways to adjacent nodes and set it equal to zero.
