Circuits: Solve Using Nodal and mesh Analysis

[Saladsamurai]

Homework Statement

Homework Equations

KCL & KVL:

The Attempt at a Solution

Ok folks I am not sure where to go from here. Someone suggested changing the 144V to its Thevenin equivalent, which I have done below. I know that I am supposed to apply KCL at each node A,B, and C. And then I represent each current in terms of voltages. Now I am a little confused as to how to proceed.

I am trying got convince myself that R1, R2, and R3 are in parallel because their leads are all connected, but I am not sure yet. The voltage drop across R1 is definitely just V_A since I can pass from A across the resistor and directly to ground. But for R2 and R3, I feel like the voltages at B and C need to be considered.

Any thoughts?

 

[gneill]

I think you meant to say that you've changed the voltage supply and its series resistance to its Norton equivalent.

Also, one leg in common does not a parallel connection make; R1, R2, and R3 are not in parallel.

With the network as shown in your second diagram, you are in a position to write the node voltage equations by inspection.

 

[Saladsamurai]

I think you meant to say that you've changed the voltage supply and its series resistance to its Norton equivalent.

Also, one leg in common does not a parallel connection make; R1, R2, and R3 are not in parallel.

With the network as shown in your second diagram, you are in a position to write the node voltage equations by inspection.

So they are not in parallel because they do not share the same voltage, correct?

I think I have it now:

Node A:

$48 - V_A/3 - (V_B - V_A)/4 - (V_C - V_A)/4 = 0$

Node B:

$(V_B - V_A)/4 - (V_C - V_B)/3 - V_B/2 = 0$

Node C:

$-V_C/12 + (V_C - V_B)/3 + (V_C - V_A)/4 = 0$

Now I need to move forward to the mesh analysis.

 

[gneill]

For components to be in parallel, both ends of each need to be directly connected to each other.

It looks like you're on the right track. Keep up the good work!

 

[rwisz]

First, let's clarify the problem statement. The problem is asking you to solve the circuit using nodal and mesh analysis. This means that you will need to apply Kirchhoff's Current Law (KCL) at each node and Kirchhoff's Voltage Law (KVL) around each loop or mesh in the circuit.

To begin, let's label the nodes A, B, and C as shown in the diagram. Next, we can apply KCL at each node to create equations for the currents flowing into and out of each node.

At node A, we have the following equation:
I1 + I2 + I3 = 0

At node B, we can use KCL to create an equation for the current flowing into node B:
I2 + I4 = 0

And at node C:
I3 + I5 = 0

Next, we can apply KVL around each loop or mesh in the circuit. Starting with the outer loop, we have:
-144 + R1*I1 + R2*I2 = 0

Moving on to the middle loop:
R2*I2 + R3*I3 = 0

And finally, the inner loop:
R3*I3 + R4*I4 + R5*I5 = 0

Now we have a system of equations that we can solve using algebraic methods or a calculator. Once we have solved for all the unknown currents, we can use Ohm's Law to find the voltage drops across each resistor and the voltage at each node.

It is important to note that R1, R2, and R3 are not in parallel. They are all in series, meaning that the current passing through each resistor is the same. This is why we can use the same current, I2, to represent the current through R2 and R3 in our equations.

I hope this helps to clarify the problem and give you a starting point for solving it using nodal and mesh analysis. Remember to always label your nodes and use consistent currents and voltages in your equations. Good luck!