Exploring the Role of Batteries in Nodal Analysis

In summary: Always mark up the circuit with arrows defining what you mean by +ve current. It does NOT matter which direction you choose for these.Then you need to mark up the circuit with arrows defining what you mean by +ve voltage across components like resistors. This must be consistent with the direction of the currents you defined above.If you follow this method there is no need to try and figure out in advance which way current will flow in any component at the outset. In some circuits that is next to impossible anyway. Using this method that will all come out in the wash. The sign of the answer and a quick look back at your marked up drawing will tell you.
  • #1
goonking
434
3

Homework Statement


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Homework Equations

The Attempt at a Solution


If I take KCL at node V1 (I'm assuming current traveling from nodeV2 to node V1)

Current in = Current out

V2 - 2volts / 2 ohms = V1 / 8 ohms

so my question is, how does the battery (2 volts in this case) play a role in nodal analysis? If I assume current enters through the negative terminal of the battery and out the poistive, it would be V2 - 2 volts / 2 ohms, correct? And V2 + 2 volts / 2 ohms if I assume current to go from V1 to V2.

is it possible to create a supernode here?
 
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  • #2
Your equation for the "current in" is incorrect. The voltage across the 2Ohm is not "V2-2volts". It's not "V2+2volts" either
 
  • #3
CWatters said:
Your equation for the "current in" is incorrect. The voltage across the 2Ohm is not "V2-2volts". It's not "V2+2volts" either
how does the battery affect the voltage of the two nodes?
does it mean the voltage on Node1 is 2 volts higher than node2?
 
  • #4
goonking said:
how does the battery affect the voltage of the two nodes?
does it mean the voltage on Node1 is 2 volts higher than node2?
Battery adds a p.d. of 2V along the path from V2 to V1, but there's also a voltage drop across the 2Ω resistance.
 
  • #5
cnh1995 said:
Battery adds a p.d. of 2V along the path from V2 to V1, but there's also a voltage drop across the 2Ω resistance.
so that means V1 - V2 = 2volts difference?

and since current flows from higher voltage to lower, the current is actually going from V1 to V2?
 
  • #6
goonking said:
so that means V1 - V2 = 2volts difference?
No. V1=V2+2V-I*(2Ω).
Conventional current direction is from V2 to V1, since conventional current flows from +ve terminal of the battery to the negative terminal.
 
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  • #7
cnh1995 said:
No. V1=V2+2V-I*(2Ω).
Conventional current direction is from V2 to V1, since conventional current flows from +ve terminal of the battery to the negative terminal.
Oh, i see, using KVL
 
  • #8
Correct.

When applying KVC and KVL there are some golden rules...

Always mark up the circuit at the outset with arrows defining what you mean by +ve current. It does NOT matter which direction you choose for these.

Then you need to mark up the circuit with arrows defining what you mean by +ve voltage across components like resistors. This must be consistent with the direction of the currents you defined above.

I repeat... It does not matter which direction you define as +ve current as long as these two steps are consistent with each other. Then later when you solve the equations if a voltage of current turns out to be -ve then you can refer back to the drawing to see what that means in practice.

If you follow this method there is no need to try and figure out in advance which way current will flow in any component at the outset. In some circuits that is next to impossible anyway. Using this method that will all come out in the wash. The sign of the answer and a quick look back at your marked up drawing will tell you.
 

Related to Exploring the Role of Batteries in Nodal Analysis

1. What is nodal analysis?

Nodal analysis is a method used in circuit analysis to determine the voltage and current at each node (connection point) in a circuit. It is based on Kirchhoff's Current Law, which states that the sum of currents entering a node must equal the sum of currents leaving the node.

2. How are batteries involved in nodal analysis?

Batteries are a type of power source commonly used in circuits, and they can play a crucial role in nodal analysis. Batteries are represented as voltage sources in circuit diagrams, and their voltage values are used in nodal analysis calculations.

3. What is the significance of batteries in nodal analysis?

Batteries are important in nodal analysis because they provide a fixed voltage value in a circuit, which can help determine the voltage and current values at other nodes. They also play a role in determining the overall power flow and performance of a circuit.

4. How does the number of batteries affect nodal analysis?

The number of batteries in a circuit can affect nodal analysis in several ways. If there are multiple batteries in a circuit, their voltage values need to be taken into account when calculating the voltage and current at each node. Additionally, the presence of batteries can change the overall topology of the circuit, requiring a different approach to nodal analysis.

5. Are there any limitations to using nodal analysis with batteries?

While nodal analysis is a powerful tool for analyzing circuits, it does have some limitations when it comes to batteries. One limitation is that nodal analysis assumes ideal batteries with no internal resistance, which may not be the case in real-world circuits. Additionally, nodal analysis may not be the most efficient method for analyzing circuits with a large number of batteries or complex topologies.

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