Principles of electricity/Voltage

Purpose
This lesson is designed to teach the fundamental characteristics of voltage.

What is Voltage?
Voltage is a measure of the electric force available to cause the movement or flow of electrons. Thus, voltage in itself implies no movement of electrons, but the potential to cause electrons to move.

Voltage measurements of direct current
When an electric force is available to cause the movement of electrons, a voltmeter is used to measure the potential. When that potential is unchanging, it is said to be a direct current or DC potential. DC electricity typically comes from a battery, but may come from a filtered, rectified power supply. More on rectification and filtering later.

Voltage measurements of alternating current
When an electrical force is available to cause the movement of electrons, it can sometimes not be measured accurately using a simple volt meter because the value is changing instant-by-instant. In a typical generator, for example, it can be changing in value between -110Volts and +110 volts in a sinusoidal (sine wave) fashion. Voltage that changes instant-by-instant, such as your household power, is called AC or Alternating Current.

In these cases, a rectified value is extracted and filtered in order that an average, 'positive' voltage value can be measured. More on the mechanism of rectification later but know that this is a method of converting AC into DC electricity.

AC riding on DC
In some cases, a DC potential is present but its value has an alternating component. Imagine a graph with a positive or negative value, but with a variation in height (vertical value) over time (horizontal value). Another way of looking at might be as fluctuations up an down upon a steady positive or negative value (example: negative 33 volts DC with a +- 6 volt variation).

Voltage, Conductors, Insulators and Semi-conductors
Voltage is a potential to move electrons. Any space that exists between two points of different voltage potential will fall into one of three categories.

A conductor presents little resistance or impedance to the flow of electricity. Copper and most metals and impure water (sweat, blood) are good conductors.

An insulator presents a great deal of resistance to the flow of electricity. Good insulators include most pure plastics, wood, ceramic, glass, rubber, air, and hard vacuum.

A semi-conductor is a material that must be coaxed into conducting by the application of a sizeable voltage.

Voltage, Resistance/Conductance and Current
In simple DC circuits, voltage, resistance and current are tightly related. As you might imagine, as resistance (to the force of voltage) goes up, the flow of electrons or current goes down. Thus, voltage (potential) and current (electron flow) are directly related, while resistance and current are inversely related. Voltage, current and resistance have been standardized in relation to one another such that we can say that Voltage = Current * Resistance. In electronics, voltage uses the symbol E, current uses I and resistance uses R. The above equation becomes E = I * R.

Voltage Calculations
Voltage is measured by placing the two leads of a multimeter at two ends of a circuit fragment. Measuring a battery voltage, for instance, we place one lead on the positive (+) terminal and another on the negative (-) terminal. If this is a 9V battery, we hope to find 9 volts.

Consider a simple light bulb connected to the two leads of the 9V battery. If you place your multimeter's leads across the battery's terminals, you are simultaneously placing the leads across the bulb's contacts. You are simultaneously measuring both the voltages across the battery and across the bulb. As you correctly imagine, the measurement should read 9 volts. Now if you add a second, identical bulb right next to the first, you still see 9 volts. However, you are measuring across 2 bulbs. Did the bulbs dim at all?

Series Resistance
Next, connect one of your two bulbs to one battery terminal only this time, take the second one and connect it between the opposite contact of the first bulb and the second terminal of the battery. Unsurprisingly, the voltage measured across the battery remains 9 volts. However, now we have a new point to measure between the two light bulbs! Taking a measure from this to either battery terminal, we find a reading of 4.5 volts, or half the total voltage.

Measuring identical resistances in series (daisy-chained resistances) should show that the value of each voltage measure is the value of the source (or total; 9V) divided by the number of identical resistances (in this case, 2 identical light bulbs; 9V/2 or 4.5V) placed in series. This works regardless of the number of resistors (a generic term for anything that conducts DC voltage and provides some resistance).

Series resistors may not be equal. How can we estimate the value we should see? Consider our example of a 9V battery and, in this case, 3 equal resistors. Effectively, we can divide this into a single resistor and two other resistors. Measuring, we find that the voltage across the first resistor is 3V and across the remaining two is 6 V. Add them up and get 9V. Seems simple. When we add the values, we always end up with the source voltage. It's not just a convenience it's a law called Kirchhoff's voltage law.

But we also see that the voltage across serial resistors can be prorated. That is, the amount of resistance across the voltage measured is equal to the fraction of its proportion of the total serial resistance. If each bulb has a resistance value of 1 Ohm (the unit of resistance) then its voltage will be 9V * (1 Ohm/3 Ohm) = 9V * 1/3 = 3V. Thus, each of the three bulbs in series drops 3 volts. Conversely, and as you would imagine, the voltage measured across two adjacent bulbs would be 6V. Did you notice something? The three bulbs were designed for 9V apiece. They experience only the force, or electrical potential, of 3 volts. These bulbs do not light at all or shine very weakly.

Parallel resistance
In a parallel circuit (or circuit fragment), two or more resistors are connected to common points at two ends. Just like the two light bulbs in our first example: the legs of the circuit experience the same voltage at their ends. But what about their resistance? How does it differ from a simple series circuit?

Considering the two bulbs across our 9V battery, we see that each drops 9 volts. However, each is equally bright or is using up an equal amount of power. Thus, we can assume that each is drawing the same amount of current. Since the resistance for each is identical, we see that the current being used by two bulbs is double what one would use. Okay, great.

9V= constant voltage / Resistance. If we assume the current is double, it is being split between the two bulbs, right? Thus, we know that, for the circuit of two resistors (our two bulbs), we have 9V = 2 * (constant current) * Resistance. Now, we know that the 9V did not change. So, we can solve for the resistance of our circuit by showing it is reduced by 1/2. Let's solve for Resistance. Resistance = 9V / 2 (constant current). In our earlier equation, we saw that at a constant current for each bulb, 9V = constant current * Resistance, which is equivalent to Resistance = 9V / constant current.

Taking these items together, we learn that identical resistances added in parallel are equal to one divided by the number of parallel circuits. In the above example, resistance is 1/2 what it was for a single bulb. It can easily be seen that a third leg would make it 1/3 the original value.

In fact, it can be demonstrated that the total resistance provided by any number of parallel legs of various resistances is equal to one over the inverse of their separate values. That is hard to write on these Wikiversity pages but I shall make the attempt.

R(total) = 1/(1/R1+1/R2+1/R3+1/R4+…+1/Rn)

In the above example, we have 1/(1/resistance + 1/resistance) = 1/(2/resistance) so we have resistance/2 or 1/2 * resistance after division. With a third leg, it would be 1/3 * resistance. If the resistance for one leg is 90 Ohms, for two it would total 45 Ohms and for 3 legs, 30 Ohms and so on.

Circuits made up of series and parallel portions When working with hybrid circuits consisting of series and parallel portions, first calculate a total for each series leg, and then calculate parallel parts. Repeat this exercise until you have calculated the value for which you are searching.

AC Voltage measurements
AC Voltage measurements are made in a nearly identical fashion to DC. However, AC uses impedance instead of resistance due to the reactions certain components have to alternating current. Know that you can use the same basic calculation steps as you did for DC, but these calculations may need to be repeated as impedance changes across different frequencies for certain circuit components.

More on impedance later.

Voltage Formulas

 * $$V = I R$$ . For a straight line conductor
 * $$V = \frac{W}{Q}$$ . For 2 parallel conductors (not explained in this lesson)
 * $$V = N L I$$ . For coil of N circles conductors (not explained in this lesson)