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Re: [Phys-L] voltage rise/drop terminology



The problem with rises and drops is that if you traverse the circuit element (resistor, source, capacitor, inductor) in the one direction, the potential will rise and in the other the potential will drop. I tell my students they must assign voltage and current symbols to each element before they start doing any calculations. Then I say the sum of the SIGNED voltages around any loop must be zero. I try to avoid the drop/rise language.

Let me first define some terminology:
1) voltage = difference in potential, so voltage is always across some circuit element or set of elements
2) current is always through an element and into or out of a junction

Voltage difference seems redundant to me, but if you want to say that a voltage at point A is the potential difference between A and a reference ground I'll accept that language. Most circuits drawn in introductory physics don't have a reference ground shown, so you can't talk about either the potential or the voltage at a point. Voltage is a potential difference between points A and B. One could talk about the difference in voltages across resistors 1 and 2. I try to avoid "voltage of resistor 1" in favor of "voltage across resistor 1."

One can assign voltages by assigning a polarity (using + and - signs [see Hayt & Kemmerly, Engineering Circuit Analysis] or bent/curved arrows [Irwin, Basic Engineering Circuit Analysis]) along with a symbol or number which represents how much higher the + side is than the - side of the element. With that terminology (the polarity and the value are inseparable), there is no ambiguity about the meaning of \Delta V or V_{ab} or \delta V or whatever you want to use. + 6V - attached to an element is exactly the same as - (-6V) + attached to the element. + (Delta V) - is the same as - (-Delta V) +, so Delta V could simply be the potential of the + side minus the potential of - side, and actually could be a negative number depending on the arbitrary assignment of the polarity directions. It makes life very simply if you stick to the inseparability of the polarity and the value.

To construct the sum, one can either use the "entering" sign of the polarity to determine whether to add or subtract the voltage value, or the "exiting" sign, but you must be consistent around the loop. Ignore any current arrows for this. You are doing a strict voltage sum.

It is essential to assign current directions AND values to each element, too. ----> 3A is exactly the same as (-3A) <-----, so the direction arrow and value are inseparable. This allows no ambiguity. Then the current 'law" becomes the sum of all currents entering any point in the circuit must equal the sum of all currents leaving that same point. The trick is to choose your points cleverly.

With this current and voltage notation, Ohms Law becomes tied to a sign convention of the voltage across and conventional current through a resistor:
Traditionally, V = IR is true if V is the number attached to the voltage polarity across the resistor and I is the number attached to the conventional current flowing in the direction from the + to the - sign (or entering the + polarity assignment or leaving the - polarity assignment).


Power calculations become simple, too. The power consumed by a device is the voltage value times the conventional current value with the current direction arrow pointing from + to -. If you get a positive number, the device is consuming power, and a negative number, the device is providing power. The total electrical powers of all devices in the circuit must add to zero. If you get a positive conventional current flowing from + to - in a battery (assuming a positive voltage value across the battery), the battery is consuming power, i.e., it is being charged.

The power consumed by an ohmic resistor is always I^2 R, where I is the current value through the resistor.


-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of Robert Cohen
Sent: Tuesday, April 08, 2014 4:54 PM
To: Phys-L@Phys-L.org
Subject: [Phys-L] voltage rise/drop terminology

When describing circuits, I refer to the voltage "rise" across a battery and the
voltage "drop" across a resistor. However, in discussions with students, I
think this may be confusing them. It makes them think that there is
something traveling from the battery, that they call voltage (and imagine as
electrons), that gets "used up" in each resistor. This leads them to several
errors. For example, it leads them to think that the last item in a line of bulbs
may not light if there is no "voltage left".
To avoid this confusion (at least until they get a better sense of what is going
on), does anyone see a problem with referring to the voltage "sources" and
"sinks", instead of "rises" and "drops"? Or is there some other language that
is clearer?


Robert A. Cohen, Department of Physics, East Stroudsburg University
570.422.3428 rcohen@esu.edu<mailto:rcohen@po-box.esu.edu>
http://www.esu.edu/~bbq

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