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### Course: Class 12 Physics (India)>Unit 3

Lesson 7: Kirchhoff's junction rule

# Kirchhoff's current law

Kirchhoff's Current Law says the currents flowing into a node must add up to zero. Created by Willy McAllister.

## Want to join the conversation?

• what is a node??
• its a point where the current will split / join.

often it is the connection between two or more conductors
• Isn't current just the rate at which the electric charge flows? So when it crosses the resistor, wouldn't the charge flow slower? But it doesn't necessarily mean that charge isn't conserved because it's just the rate at which it flows that has decreased, no?
Thanks very much
• The best way to see that Kirchhoff must be right is to think about what it would mean if he was wrong. If you have more current flowing into a point than out of it (for example if the point is somewhere the charge starts to flow slower), then the charges would start building up in in front of the point. Eventually there would be so much charge packed together that lightning would start shooting out of the circuit (assuming you could keep the current going that long). The fact that we don't see lighting shooting out of resistors indicates that the current flows at the same rate before and after the resistor.

Now why is it so? The reason is that electrons repel each other. The electrons do get slowed down by the resistor. In fact, that is what a resistor is: a "brake" slowing down electrons by having them collide with the atoms it's made of, turning some of their kinetic energy into heat. But when an electron slows down in the resistor, the electron right behind it bumps into it, and since electrons repel, it also gets slowed down. This electron then slows down the electron behind it again, and so it goes around the entire circuit. You can think of the electrons in the circuit as marbles packed tightly in a tube. If you slow down one of them, you slow down all of them.

So yes, a resistor makes the charge flow slower, but it makes the charge flow slower in the entire circuit it is part of, not just after the resistor.
• is it necessary that in every condition this law is applied ? like if i change the physical conditions like temperature does this law will still be applied??
• Hello DeepShankarPratap,

Kirchhoff's current and voltage laws are ALWAYS true.

On a related note, Ohm's law is also true. However, many physical systems have resistance / impedance that changes with temperature.

Regards,

APD
• Ok I am confused around , where that one current equals -3. I get how current in general can be negative, but I am confused on how the current going in is equal to zero and if the current going on/out is always equal to zero.
• Another way of putting it is all the current going in is equal to all the current going out. So if you have 3A of current going into a node, then there must be 3A of current going out of the node. The reason Sal says that i = -3A is because he defined the direction of current i to be going in, so negative would mean the direction is going in the opposite direction as it was defined.
• At , does the expression for Kirchhoff's current law equal zero?
• Iin = Iout, here in the two examples Iin = 0 then Iout = 0. In the other example, Iout = 0, then Iin =0. So the general expression for kirchoff's current law is Iin = Iout (current in, current out)
(1 vote)
• The Kirchhoff's current law only works for Direct Current (DC), right?
• How to find the current between two nodes ?
• Hello Pranjal,

It depends on the circuit configuration. Series circuits are easy - the current is the same everywhere in the circuit. Things get complicated from here when we start to add parallel plus series branches. The tools of choice are mesh analysis, nodal analysis, and superposition.

Please look for these tools here on the Khan Academy EE section.

Regards,

APD
• why cant we take i1+i3=i2
• Sorry for the late response.

If you switch a number with the plus side to the other side it will switch to negative so you can do: i1 - i3 = i2, but you can't do i1 + i3 = i2. That could also depend: maybe you switch the names around then you can do that otherwise it is ILLEGAL in physics.
• Why is the sum of the current equal to 0?
• because charge can't be created or destroyed, so however much charge goes into that junction has to also come out
• What is Mutual inductance?
• Hi MD,

Mutual inductance describes the operation of a transformer.

Here we have two coils of wire. A changing magnetic field in one coil causes a voltage change in the other.

Regards,

APD