How Does Nodal Analysis Determine Currents in a Circuit with Multiple Resistors?

[nisal5500]

Homework Statement

Using Nodal analysis, determine the current through each resistor, for this circuit. Could you please show the KCL working out.I need the answers Please help me i am helpless with nodal analysis consist of a current source.Thanks in advance :) !.please help me.

r1=120
r2=360
r3=330
r4=820
r5=100
r6=470
i1=15mA

Homework Equations

i1 + i2 + i3 = 0 ?

3) The attempt at a solution
first i converted the current sources and apply kcl for node 1.
For node1:
(9-v1)/120+(-4.95-v1)/560=0
so v1=7.41176v
For node 2:
v2/820+(5--v2)/570=0
so v2=3v.

I assumed that all currents are comming in.

I really want the answers please [/quote]

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Please click on the image to zoom

 

[gneill]

Homework Statement

Using Nodal analysis, determine the current through each resistor, for this circuit. Could you please show the KCL working out.I need the answers Please help me i am helpless with nodal analysis consist of a current source.Thanks in advance :) !.please help me.

r1=120
r2=360
r3=330
r4=820
r5=100
r6=100
r7=470
i1=15mA

Homework Equations

i1 + i2 + i3 = 0 ?

3) The attempt at a solution
For the 1st question i gt v1=2.7794*10^-3v and v2=-0.072194v.

View attachment 55774


I really want the answers please

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Please click on the image to zoom

You'll have to show an attempt so that we can know how to help; we won't do your homework for you here.

Presumably the list of resistances you've given are for the first circuit, but you've listed seven resistors when the circuit shows only six Also, it's difficult to make out the values on the voltage supplies from the image; you'll have to clarify them.

Start by identifying your reference node and labeling the others. Then make an attempt at writing node equations so we can see your level of understanding. If you have absolutely no idea what any of this means, you'll have to review your text and notes first.

 

[nisal5500]

You'll have to show an attempt so that we can know how to help; we won't do your homework for you here.

Presumably the list of resistances you've given are for the first circuit, but you've listed seven resistors when the circuit shows only six Also, it's difficult to make out the values on the voltage supplies from the image; you'll have to clarify them.

Start by identifying your reference node and labeling the others. Then make an attempt at writing node equations so we can see your level of understanding. If you have absolutely no idea what any of this means, you'll have to review your text and notes first.

first i converted the current sources and apply kcl for node 1.
For node1:
(9-v1)/120+(-4.95-v1)/560=0
so v1=7.41176v
For node 2:
v2/820+(5--v2)/570=0
so v2=3v.

 

[gneill]

first i converted the current sources and apply kcl for node 1.
For node1:
(9-v1)/120+(-4.95-v1)/560=0
so v1=7.41176v
For node 2:
v2/820+(5--v2)/570=0
so v2=3v.

It's not necessary to convert the current source; You're writing KCL equations for nodes, and the given current source just needs to be added to or subtracted from the current totals for the nodes it connects to. But it's okay to convert wish, it's just a bit of extra work for you. You should make clear what the converted source is. What's its potential, resistance, and orientation?

You haven't specified which nodes are which, so it's difficult to tell what your equations represent. Where's the reference node? Which node is node 1? Which is node 2? What's the value of the E1 source (looks like it might be 9V from the equations you wrote).

 

[DeeNos]

in for a clearer view of the solution.

Nodal analysis is a powerful technique used in circuit analysis to determine the voltage and current at different nodes in a circuit. It is based on the concept of Kirchhoff's Current Law (KCL), which states that the sum of all currents entering a node must equal the sum of all currents leaving the node.

In this circuit, we have two nodes - node 1 and node 2. Using KCL, we can write the following equations for each node:

Node 1:
i1 + i2 + i3 = 0
Where i1 is the current through the 15mA current source, i2 is the current through resistor R5, and i3 is the current through resistor R6.

Node 2:
i2 + i4 + i5 = 0
Where i4 is the current through resistor R1, i5 is the current through resistor R2, and i6 is the current through resistor R3.

To solve for the unknown currents, we can use Ohm's law (V=IR) and substitute the values given in the problem to get the following equations:

Node 1:
15mA + (9V - v1)/120 + (-4.95V - v1)/470 = 0
Simplifying, we get:
4.95mA - v1/120 - v1/470 = 0
Bringing the variables to one side, we get:
-0.00833v1 = -4.95mA
Solving for v1, we get:
v1 = 594.059mV

Now, we can use this value to solve for the current through R5 and R6:
i2 = (9V - v1)/120 = 4.05mA
i3 = (-4.95V - v1)/470 = -10.531mA

Node 2:
i2 + (5V - v2)/360 + (v2 - 3V)/330 = 0
Simplifying, we get:
i2 + v2/360 - v2/330 = 0.01364A
Substituting the value of i2 we found earlier, we get:
4.05mA + v2/360 - v2/330 = 0.01364A
Bringing the variables to one side, we get:
-0.00303