Diving Deeper
2. Setting the Stage
Before we can jump into writing equations, we need to pick a reference node. This is often referred to as the "ground" node, and we assign it a voltage of 0 volts. Think of it as the baseline or starting point for all other voltage measurements in the circuit. Choosing a good reference node can make the problem simpler. Usually, the node with the most connections to other circuit elements is a good choice, as it can simplify the resulting equations.
Once you've selected your reference node, you can then label the voltages at all the other nodes in the circuit. These are the unknown voltages we're trying to find. It's helpful to use symbols like V1, V2, V3, etc., to represent these node voltages. Now, imagine you're creating a map of the circuit, labeling each intersection with a voltage value. This "voltage map" will be key to understanding the current flow.
Now, for each node (except the reference node), we'll apply KCL. This means we'll write an equation stating that the sum of the currents entering the node equals the sum of the currents leaving the node. Remember Ohm's Law (V = IR)? We'll use that to express the currents in terms of the node voltages and the resistances (or other impedances) in the circuit. It's like translating the circuit diagram into mathematical equations.
By applying KCL to each node, we'll end up with a system of simultaneous equations. The number of equations will be equal to the number of unknown node voltages. We can then solve this system of equations using various methods, such as substitution, matrix algebra, or computer-aided tools. Once we know the node voltages, we can use Ohm's Law again to find the currents flowing through any circuit element in the circuit. And just like that, the circuit is solved!
