Question about circuits (currents going into nodes)

[doctordiddy]

So according to kirchhoffs junction rule, all currents entering a node must be equal to currents exiting a node. In this example

http://imgur.com/4Zqb21A

If we take a node as the point between the 4 ohm resistor, 5 ohm reisistor, and the 20V battery, how would you be able to determine an equation or currents?

For example, if I1 is the current through the 2ohm battery, I2 the current through the 4ohm, and I3 the current through the 5 ohm, how can you write this relationship?

I1=I2+I3?
I2=I3+I1?

How can you determine which currents are entering and exiting a node?

Thanks for any help

 

[SammyS]

So according to kirchhoffs junction rule, all currents entering a node must be equal to currents exiting a node. In this example

http://imgur.com/4Zqb21A

If we take a node as the point between the 4 ohm resistor, 5 ohm reisistor, and the 20V battery, how would you be able to determine an equation or currents?

For example, if I1 is the current through the 2ohm battery, I2 the current through the 4ohm, and I3 the current through the 5 ohm, how can you write this relationship?

I1=I2+I3?
I2=I3+I1?

How can you determine which currents are entering and exiting a node?

Thanks for any help

You must pick a definite direction for each of those currents.

 

[doctordiddy]

how would you tell which two are going in the same direction and which one is going in the opposite direction?

 

[SammyS]

how would you tell which two are going in the same direction and which one is going in the opposite direction?

It's totally up to you to pick the direction, if it's not given to you.

Then you work out the problem, finding all the currents. Some may turn out to be negative, which simply means the current actually flows opposite to the direction you chose.

 

[Nickie]

I am happy to answer your question about circuits and currents entering and exiting nodes. Kirchhoff's Junction Rule states that the sum of all currents entering a node must be equal to the sum of all currents exiting that node. This rule is based on the principle of conservation of charge, which states that charge cannot be created or destroyed, only transferred.

In the given example, the node between the 4 ohm resistor, 5 ohm resistor, and 20V battery can be represented as a closed loop. Using Kirchhoff's Junction Rule, we can write the following equation:

I1 + I2 + I3 = 0

This means that the sum of all currents entering the node must be equal to zero, as there is no charge buildup or loss at the node.

To determine the relationship between the currents, we can rearrange the equation to solve for one of the currents in terms of the other two. For example, if we solve for I1, we get:

I1 = -I2 - I3

This means that the current through the 2 ohm battery (I1) is equal to the negative sum of the currents through the 4 ohm resistor (I2) and 5 ohm resistor (I3).

In terms of which currents are entering and exiting a node, we can determine this based on the direction of current flow in the circuit. Current always flows from a higher potential (in this case, the 20V battery) to a lower potential (the resistors). So, in this circuit, I1 and I2 are entering the node, while I3 is exiting the node.

I hope this helps clarify the relationship between currents in a circuit and how to determine which are entering and exiting a node. Let me know if you have any further questions.