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# Node voltage method (steps 1 to 4)

The Node Voltage Method solves circuits with the minimum number of KCL equations. Steps 1 to 4 out of 5. Created by Willy McAllister.

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• Question about Step 4, when writing KCL, why does i1 = (V1 - V2)/R1 and not just V1/R1? Why is it the difference between that and V2/R2? • Hello Arig,

The voltage V2 is likely a non zero voltage. And so we must account for the actual voltage drop across R1:

i1 = change_in_voltage / resistance

Recall that KCL is concerned with the currents at a particular node. "The sum of the currents must equal zero!"

i1 + I2 + I3 = 0
where:
i1 = (V2 - V1) / R1
i2 = (V2 - 0) / R2
i3 = iS

Regards,

APD
• I'm a little unsure as to how you could say just from visual inspection that the node voltage V1 = 15volts. If the voltage has to add up to zero would that mean V2 = 0 volts? • Good question. At , I know V1 = 15V because there is an ideal 15V voltage source connected directly between the reference node at the bottom, and node 1. You asked about summing the loop voltages: "the voltage has to add up to zero." . Be sure to phrase KVL as, "the element voltages around a loop add up to zero." Remember, the element voltages (Vr1 and Vr2) are the voltages across each resistor element. These are the voltages you put into a KVL equation. Element voltages are not always the same as node voltages (v1 and v2). KVL around the loop would be V1 + Vr1 + Vr2 = 0. If you want, you could replace element voltage Vr2 with node voltage V2, since they mean the same thing.
• At , I don't understand clearly why i1 equals (V1-V2)/R1. • V1 and V2 are "node voltages". That means they are measured with respect to the reference node (ground). This is suggested by the two orange arrows that start at the ground node and curve up to each node.

Resistor R1 is connected between node 1 and node 2. The "element voltage" that appears across R1 is the difference of the two node voltages, V1-V2. Using Ohm's Law you compute the current through R1 as

i = Voltage across resistor / R
i = (V1 - V2) / R
• What is ground meant to be in our circuits, i tries looking up on the internet and it tells me ground is the point in circuit that is meant to be at 0v. However why do we need a point on the circuit that is at 0v, and isn't the negative terminal of the battery at 0v with respect to the positive, so do i take it that the negative terminal of our battery is ground?? • Ground is used to establish a reference voltage somewhere in the circuit. A story: suppose you are on the second floor of a building and want to answer the question, "How high is the top of your head?" One end of the ruler will be at the top of your head. Where does the other end of the ruler go? The floor you are standing on? The ground floor? The center of the Earth? You have to decide on a reference level. Your decision about where to put the other end of the ruler establishes the reference height from which you will measure all heights. The reference height = 0, by definition. That's what ground does in a circuit.
• Of course in Germany (or I guess in Middle Europe in general) the voltage arrows point in the other direction. Usually without a change in sign for the voltage, the current flow remains unchanged. Compare to: https://de.wikipedia.org/wiki/Netzwerkanalyse_(Elektrotechnik) The voltage arrow points from positive potential to negative potential, as the technical current flow. This way, the current flow and the voltage drop in DC circuits match (besides the voltage source kind of). Not exactly a question, but still good to know. • Isn`t the node an intersection between 3 branches? Why is 1 a node? • I think understand why i1 = (V1-V2)/R1, since the i1 is connected to nodes a and b, but how did you know it was V1-V2 and not V2-V1? • What exactly is a current source? I understand a voltage source such as a battery or power supply, but am not clear on what a current source might be. • Hey, I still do not get why I1 is equal to (V1-V2)/R1, by KCL we know that the current going in the first node is equal to Is, and it is possible to obtain Is by dividing Vs/R1 therefore I1 the value going into the node should be equal to Is. Hope I made my question clear, hope I hear from you soon.  