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## Class 12 Physics (India)

### Unit 3: Lesson 7

Kirchhoff's junction rule

# Kirchhoff's junction rule review

Review the key terms and skills related to Kirchhoff's junction rule.

## Key terms

### Junction

Intersection of three or more pathways in a circuit. Typically represented by a dot on a circuit diagram. Also called a node.
Figure 1. Two junctions represented by dots and the current pathways highlighted.

### Branch

A path connecting two junctions.
Figure 2. Two branches in a circuit, each highlighted in a different color.

## Kirchhoff’s junction rule

Kirchhoff’s junction rule says that the total current into a junction equals the total current out of the junction. This is a statement of conservation of charge. It is also sometimes called Kirchhoff’s first law, Kirchhoff’s current law, the junction rule, or the node rule. Mathematically, we can write it as:
I, start subscript, start text, i, n, end text, end subscript, equals, I, start subscript, start text, o, u, t, end text, end subscript
Junctions can’t store current, and current can’t just disappear into thin air because charge is conserved. Therefore, the total amount of current flowing through the circuit must be constant.
Figure 3: Kirchhoff’s junction rule says that the current flowing into the node, i, start subscript, 1, end subscript and i, start subscript, 2, end subscript, must be equal to the current flowing out of the node, i, start subscript, 3, end subscript and i, start subscript, 4, end subscript.
For the total current in Figure 3, we can write the relationship between the current going into and out of the node as:
\begin{aligned}I_\text {in} &= I_\text {out}\\ \\\\ i_1+i_2 &= i_3+i_4\end{aligned}
For example, in Figure 4, the current into the node equals the current out of the node.
Figure 4: The current into the node equals the current out of the node.
The current into the node is 3, start text, A, end text. There are two branches out of the node. The current across resistor R, start subscript, 2, end subscript is 2, start text, A, end text and the current across resistor R, start subscript, 3, end subscript is 1, start text, A, end text, so we can write:
\begin{aligned}i_\text{in} &= i_\text {out} \\\\ 3\,\text A &= 1 \,\text A + 2\,\text A\\\\ 3\,\text A &= 3\,\text A \goldD{\leftarrow \text {yes!}}\end{aligned}

For deeper explanations, see our video on Kirchhoff's junction rule (or current law).
To check your understanding and work toward mastering Kirchhoff's junction rule, check out the Kirchhoff's junction rule exercise.

## Want to join the conversation?

• How do resistors decrease voltage, but keep current the same?
• Resistors do NOT decrease the voltage. Resistors make it harder for electrons to flow. Thus, if you want to keep the current constant while changing the other variables you can do one of 2 things:

Increase the voltage (which means using a more powerful battery) while increasing the resistance (using a resistor made of a more insulant material). In this case you would have an increased force pushing the electrons to flow but, at the same time, you would have a greater resistance to such a flow, leading to the same stream of electrons moving across the resistor

Decrease the voltage, pushing the electrons less fiercely and thus decrease the resistance to make sure the number of electrons flowing remains the same.

The first few lessons about Ohm's law explain this quite nicely, you may want to review them to get a better understanding.
• Does the thermal energy generated from current flow in the resistor affects the out current ?
• The current that goes inside one end of the resistor is the same as the current that comes out from the other end, this is always true because of the law of conservation of charge. But how is the thermal energy dissipated related to the current that flows through the resistor?
Let's take it a little step further: recall the relationship

P = I DV
and apply Ohm's law to get its twin equation

P = I^2 R
Where the power is the thermal energy generated per unit of time. If this sounds completely new to you check out the video on electric power https://www.khanacademy.org/science/ap-physics-1/ap-circuits-topic/introduction-to-dc-circuits-ap/v/electric-power

Now, what happens if we change the current that flows through the resistor? Well, to do that we need to either change the voltage (using a different battery) or the resistor (using a resistor with different resistivity) while keeping the other component the same.
If we use a more powerful battery there will be more current flowing through the same resistor and the thermal energy generated would be greatly increased because the power depends to the current squared.
If we keep the same battery but choose a resistor with lower resistivity we would see that the current increases again, making the power increase greatly, but remember that we reduced the resistance and thus the increase in power is damped out a little by the decrease in resistance.
There are other cases to explore but the two equations you see on top and Ohm's law will help you figure everything out by yourself, have fun :)
• We know resistance decrease or oppose the current flow. Then how the current I remain the same after passing through different registers and junctions? ( on practice example i thought it was voltage which does not affect by the resistance!)
(1 vote)
• Resistance does oppose the current flow. Although in a series circuit the current is the same at all points in the circuit, the resistor resists the amount of current that can flow. For example lets say you had a circuit with a battery of voltage 10 V and there was a 2Ω resistor. Using Ohm's law, you can find that the current will be 5 A. At all points in the circuit, the current will be 5 A. Now lets say that you replace the 2Ω resistor with a 5Ω resistor. Now, the current will be 2 A at all points in the circuit. The current is still the same at all points in the circuit, but the larger resistance means that the current will be more restricted. Hope this helps!
• So I heard that Kirchoff's Junction Rule can be reversed, like
Iout = Iin
but this doesn't make sense, because you could have more current joining in at the end of one junction "end point"
If you had 2 junctions, close enough so that their ends were touching, it could interfere with the amount of current out.
If the circuit looks like this,(~ is the battery) where there are dashes, close to the end, but not at the end, is where there could be the 2 junctions. So, did I hear wrong, or is my thinking wrong? Thanks for your help!
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(1 vote)
• The SUM of the out is equal to the in. That is very important, because you are not just selecting one of your end points, you are adding up all of them. Kirchoff's Junction Rule holds true.
• This was a very good lesson without getting too Mathematically intense, I was able to picture Kirchoff laws and relate the at least visually to fluid flow
(1 vote)
• Would the same apply to the other side? like as it reaches the negative output?
(1 vote)