Kirchoff's Circuit Law

In summary: It's just a diagram convention to draw a node-dot where wires meet, but it actually includes the wires themselves.
  • #1
yaro99
75
0

Homework Statement


Determine the values of the other currents in Figure P1.37, given that ia = 2 A, ic =−3 A,
ig = 6A,and ih= 1A.

ealHzUE.png



Homework Equations


∑currents entering a node = ∑currents exiting the node


The Attempt at a Solution



I used Kirchoff's Circuit Law on each of the outer nodes:

if = ig + ih = 6 + 1 = 7A

ia + id = if
2 + id = 7
id = 5A

ic + ih= ie
-3 + 1 = ie
ie = -2A

ib = ia + ic = 2 - 3 = -1A

I think I may have went wrong somewhere, because when I apply KCL to one of the inner nodes I get this:

ie + ig = id (?)
-2 + 6 ≠ 5
 
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  • #2
yaro99 said:

Homework Statement


Determine the values of the other currents in Figure P1.37, given that ia = 2 A, ic =−3 A,
ig = 6A,and ih= 1A.

ealHzUE.png



Homework Equations


∑currents entering a node = ∑currents exiting the node


The Attempt at a Solution



I used Kirchoff's Circuit Law on each of the outer nodes:

if = ig + ih = 6 + 1 = 7A

ia + id = if
2 + id = 7
id = 5A

ic + ih= ie
-3 + 1 = ie
ie = -2A

ib = ia + ic = 2 - 3 = -1A

I think I may have went wrong somewhere, because when I apply KCL to one of the inner nodes I get this:

ie + ig = id (?)
-2 + 6 ≠ 5

There's only one "inner node" where B, D, G, and E meet; despite there being two connection dots there, they are all one single conducting path with no components in between.

So, your node equation needs to account for ##i_b##, too.
 
  • #3
gneill said:
There's only one "inner node" where B, D, G, and E meet; despite there being two connection dots there, they are all one single conducting path with no components in between.

So, your node equation needs to account for ##i_b##, too.

Aha, in that case it will be
-2 + 6 = -1 + 5
4 = 4

How do I know that the node includes ##i_b##, is that current not affected by the current ##i_d##?

Is the point connecting B and D not a node?
 
  • #4
The two inner nodes are actually one node.
You missed a current: two currents go into the node and two currents go out of the node.

[edit]gah: too slow!
 
  • #5
yaro99 said:
How do I know that the node includes ##i_b##, is that current not affected by the current ##i_d##?

Is the point connecting B and D not a node?

So long as there is a continuous conducting path it is all one node. A node is not a dot on the diagram, it's the entire continuous conducting path.

To make it more clear, you can shift component E over a bit as follows:

attachment.php?attachmentid=65959&stc=1&d=1390527029.gif


The wiring in green is continuously connected, so it's all one node.
 

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  • #6
gneill said:
So long as there is a continuous conducting path it is all one node. A node is not a dot on the diagram, it's the entire continuous conducting path.

To make it more clear, you can shift component E over a bit as follows:

attachment.php?attachmentid=65959&stc=1&d=1390527029.gif


The wiring in green is continuously connected, so it's all one node.

Ah, yes that confused me a bit. It makes sense now thanks!
 
  • #7
Great - the other way to look at it is to add an extra current arrow ##\small{i_0}## in the gap between the "two" center nodes. You can tell which direction it has to point in by looking at the other currents - but it actually doesn't matter:

Current in = current out:
... so on the left node you get ##i_0 = i_b+i_d##
... and for the right node you get ##i_0=i_g+i_e##

... eliminate the ##\small{i_0}## term gives you ##i_b+i_d = i_g+i_e##

and it all comes out in the wash ;)

It's just easier to realize that the nodes for Kirkoffs laws actually include the entire wire between components. Thus two drawn node-symbols, on the diagram, that have no components between them, are one and the same.
 

1. What is Kirchoff's Circuit Law?

Kirchoff's Circuit Law, also known as Kirchoff's Current Law (KCL) and Kirchoff's Voltage Law (KVL), are fundamental laws in circuit analysis that govern the behavior of electric currents and voltages in a closed circuit.

2. What is the difference between KCL and KVL?

KCL states that the sum of all currents entering a node in a circuit must equal the sum of all currents leaving that node. KVL states that the sum of all voltage drops around a closed loop in a circuit must equal the sum of all voltage sources in that loop.

3. How do I apply Kirchoff's Circuit Law in circuit analysis?

To apply KCL and KVL, you must first draw a circuit diagram and label all the components and nodes. Then, write down the equations for KCL and KVL for each node and loop, respectively. Finally, solve the equations simultaneously to find the values of unknown currents and voltages.

4. Can Kirchoff's Circuit Law be applied to all circuits?

Yes, Kirchoff's Circuit Law can be applied to all types of circuits, including DC circuits, AC circuits, and complex circuits with multiple components and loops. However, the laws may become more complicated and require advanced techniques for more complex circuits.

5. What are some real-world applications of Kirchoff's Circuit Law?

Kirchoff's Circuit Law is used in a variety of real-world applications, such as designing and analyzing electrical circuits in electronics, telecommunications, and power systems. It is also used in industries such as aerospace, automotive, and medical devices to ensure the proper functioning of electrical systems and components.

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