Why Are We Interested In Node Voltages?

[xatu]

Question: When we discuss voltages in a circuit, why are we particularly interested in the voltages at nodes?

For example, Kirchoff's Voltage Law states that the sum of the voltages around in closed circuit is 0. This implies that every source/load voltage in a circuit is located between two or more nodes, yes?

This may be a fairly obvious question to some, but I feel like it is has been introduced with no real explanation.

 

[berkeman]

Question: When we discuss voltages in a circuit, why are we particularly interested in the voltages at nodes?

For example, Kirchoff's Voltage Law states that the sum of the voltages around in closed circuit is 0. This implies that every source/load voltage in a circuit is located between two or more nodes, yes?

This may be a fairly obvious question to some, but I feel like it is has been introduced with no real explanation.

I prefer to use KCL equations to solve most circuits. The KVL equations are less intuitive to me. Node voltages are important for writing the KCL equations.

Either version (KCL or KVL) is a very useful way to solve circuit network problems. It's so nice to have a systematic equation-based method of solving circuits for their voltages and currents.

 

[AlephZero]

A different way to answer the question is that in real circuits, the easiest things to measure for fault-finding etc are voltages - either DC with a meter, or AC with an oscilloscope.

To measure current, often you have to disconnect some part of the circuit to insert a meter. If you are looking for a fault that is time consuming, and you risk causing more faults by unsoldering components and replacing them, etc.

 

[xatu]

Thanks for the help guys.

So basically it seems that our concern with node voltages is somewhat arbitrary, mainly owing to its ease of measurement. Right?

 

[berkeman]

Pretty much. In a SPICE simulator you can monitor both voltages and currents. But as Aleph points out, voltages are mostly what you monitor in real life with your instrumentation.

 

[xatu]

I had the following thought when thinking about this lately:

Would a connecting wire in a circuit even have a voltage across it? Conducting wires have practically no resistance, and, by Ohm's Law (V=iR), have V≈0 for any i?

 

[gneill]

I had the following thought when thinking about this lately:

Would a connecting wire in a circuit even have a voltage across it? Conducting wires have practically no resistance, and, by Ohm's Law (V=iR), have V≈0 for any i?

Sure. There's a difference between "practically no resistance" and "no resistance". In many cases the inherent resistance of wires is negligible compared to other resistances in the circuit. Note that this is not the case for some very practical things such as long distance power transmission lines!

Whether or not you have to take into account the real physical properties of conductors depends upon the circumstances and the level of detail you need to account for. Conductors also have inductance and capacitance (to surrounding conductors) that may come into play at high frequencies. Circuit layout can be an "interesting" challenge at high frequencies!

 

[CWatters]

I had the following thought when thinking about this lately:

Would a connecting wire in a circuit even have a voltage across it? Conducting wires have practically no resistance, and, by Ohm's Law (V=iR), have V≈0 for any i?

What gneill said.

This is an important issue for the power distribution grid. Real wires have some small resistance so the voltage might start off as 110V at a local transformer but it will be somewhat less by the time it get to your house due to the voltage drop down the wire. Typically they have to correct for this by increasing the voltage at the transformer so that you do get 110V at your house.

 

[rude man]

What gneill said.

This is an important issue for the power distribution grid. Real wires have some small resistance so the voltage might start off as 110V at a local transformer but it will be somewhat less by the time it get to your house due to the voltage drop down the wire. Typically they have to correct for this by increasing the voltage at the transformer so that you do get 110V at your house.

That sounds questionable, since the voltage drop across the transformer-to-house wiring is obviously directly proportional to the load current, which can be anywhere from close to zero A to 100 A or more.

 

[CWatters]

That sounds questionable, since the voltage drop across the transformer-to-house wiring is obviously directly proportional to the load current, which can be anywhere from close to zero A to 100 A or more.

Yes my bad description. I didn't mean to imply this is something they do in real time. I'm in the UK where local transformers feed groups of houses. As more houses are added it's possible for the delivered voltage to drop out of limits at times of peak loads. They fix this by adjusting the transformer voltage by taking a different tap. This is typically done when new houses are added.

 

[gneill]

That sounds questionable, since the voltage drop across the transformer-to-house wiring is obviously directly proportional to the load current, which can be anywhere from close to zero A to 100 A or more.

Transformer-to-house distance is usually trivial compared to the long haul power transmission lines from remote generating stations to a local substation. Substation transformers take the really high tension supplied and step it down to a more modest (but still high) voltage for distribution on poles as the "high tension" wire running at the top. This wire is tapped periodically to supply a pole transformer to boost the voltage on the 3-wire network lower down the pole to which house connections are made. Pole transformers are pretty plentiful in a typical suburban neighborhood. If you live in a house in a typical suburb you can probably see at least one pole transformer from there.

For 200 A house service the wire from the pole is something like a 2/0 gauge with a resistivity of about 0.26 Ω / km. If your pole is 30 m or so from the house the wire resistance amounts to about 8 milliohms per leg. So not much voltage drop there, even at full rated load.

 

[rude man]

Yes my bad description. I didn't mean to imply this is something they do in real time. I'm in the UK where local transformers feed groups of houses. As more houses are added it's possible for the delivered voltage to drop out of limits at times of peak loads. They fix this by adjusting the transformer voltage by taking a different tap. This is typically done when new houses are added.

OK, but is there then not a danger of overly high voltage when all the houses are running light loads? I suppose the law of averages comes into play here ...