Hello everyone. In this video, we revise Kirchhoff's circuit laws. The first Kirchhoff law is the current law, Kirchhoff current law. So, Kirchhoff current law signifies that at each node in our circuit network, the summation of all current entering this node must equal to zero. Or, in other words, when you do summation of current entering the node, this is equal to the current exiting the node. This describes that at a node, there is no storage of energy, and charges cannot be stored in a node. So, charges entering the node will be leaving the node into a branch.

Previously in this course, we talked about the KCL using resistors, but actually, Kirchhoff's current law is generalizable to any device. So here, I have a generic circuit. I have devices. So, at node A, we still can write that I1, which is entering, should equal to I2, which is leaving, regardless of the nature of the device in which I1 is going through and the nature of the device that I2 is going through. This can be a resistor, can be an inductor, can be a capacitor. Same for node B.

So, at node B here, we have I4 entering, I3 leaving, and I2 entering. So, summation of current entering, I2 + I4, should equal to I3, which is leaving. Again, the intuition behind that is that no energy or no charge is being stored at that node. Finally, at node C (this is our node C), we have I3 entering, and we have I1 and I4 leaving (I3 = I1 + I4).

As I mentioned, this KCL is generalizable for any device that we studied thus far in this course. So, if this is a capacitor, for example, at node A, we have I1 entering, which is equal to I2. If this device here, in which we have I1, is a capacitor, then this I1 would be a function of time. I would vary over time, and as a result, I2 would also vary over time. Also, we know that this IC is related to the voltage across the capacitor, is equal to C dV_C/dt, and this is equal to I2(t).

To complete the G, so this gives us a first-order differential equation in which we can use to solve for the capacitor voltage if we already know how I2 looks like.

The second Kirchhoff law that we have is the voltage law. The voltage law tells you that the voltage drop within a loop across all elements should sum to zero. So, in this figure, we have two loops. This is loop number one, and this is loop number two.

So, in loop number one, if you wrote a KVL, it should be: 
-V3 + V1 - V4 - V6 = 0.

Likewise, for loop two, we have:
V4 - V2 + V5 = 0.

And similar to KCL, KVL is also applicable not only to resistors but also to all circuit elements that we studied in this class, like the capacitor and the inductor.

So, for example, if this element here has an inductor L, so if we wrote the KVL for loop number one, we have:
-V3 + V1 - V4 - V6 = 0.

This V3 is the inductor voltage, and we know that the inductor voltage is a function of time. So, this equation here would be entirely a function of time T, meaning that V1, V4, and V6 are no longer constant. Instead, they vary over time. Moreover, we can relate V3, which is the voltage across the inductor, to the inductor current by writing it as L dI_L/dt.

So, this is another equivalent representation for this loop, assuming that element number three is an inductor. From here, you can see that we have a differential equation that has I_L net, and we can solve for I_L if needed.

So, in conclusion, we revised KCL and KVL. KCL depends on the fact that no energy or charge is stored at a node. As a result, all current entering the node should be leaving that node. And KVL tells us that the voltage drop across elements within the same loop should sum up to zero. Both laws are generic and generalizable to resistors, inductors, and capacitors.

Thank you.