# Voltage: Wikis

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# Encyclopedia

International safety symbol "Caution, risk of electric shock" (ISO 3864), colloquially known as High voltage.

The voltage between two points is a short name for the electrical force that would drive an electric current between those points. Specifically, voltage is equal to energy per unit charge.[1] In the case of static electric fields, the voltage between two points is equal to the change in electrical potential difference between those points. In the more general case with electric and magnetic fields that vary with time, the terms are no longer synonymous, [2]

Electric potential is the energy required to move a unit electric charge to a particular place in a static electric field. [3]

Voltage can be measured by a voltmeter; real voltmeters approximate ideal voltmeters. The unit of measurement is the volt.

## Definition

The electric field around the rod exerts a force on the charged pith ball, in an electroscope.

The voltage between two ends of a path is the total energy required to move a unit electric charge along that path, divided by the magnitude of the unit charge. Mathematically this is expressed as the line integral of the electric field and the time rate of change of magnetic field along that path. In the general case, both a static (unchanging) electric field and a dynamic (time-varying) electromagnetic field must be included in determining the voltage between two points.

## Historical definitions

Historically this quantity has also been called "tension"[4] and "pressure". Pressure is now obsolete but tension is still used, for example within the phrase "High Tension" (HT) which is commonly used in thermionic valve (vacuum tube) based electronics.

## Hydraulic analogy

A simple analogy for an electric circuit is water flowing in a closed circuit of pipework, driven by a mechanical pump. This can be called a water circuit. Voltage difference between two points corresponds to the water pressure difference between two points. If there is a water pressure difference between two points, then water flow (due to the pump) from the first point to the second will be able to do work, such as driving a turbine. In a similar way, work can be done by the electric current driven by the voltage difference due to an electric battery: for example, the current generated by an automobile battery can drive the starter motor in an automobile. If the pump isn't working, it produces no pressure difference, and the turbine will not rotate. Equally, if the automobile's battery is flat, then it will not turn the starter motor.

This water flow analogy is a useful way of understanding several electrical concepts. In such a system, the work done to move water is equal to the pressure multiplied by the volume of water moved. Similarly, in an electrical circuit, the work done to move electrons or other charge-carriers is equal to "electrical pressure" (an old term for voltage) multiplied by the quantity of electrical charge moved. Voltage is a convenient way of measuring the ability to do work. In relation to "flow", the larger the "pressure difference" between two points (voltage difference or water pressure difference) the greater the flow between them (either electric current or water flow).

## Simple applications

Common usage (that "voltage" usually means "voltage difference") is now resumed. Obviously, when using the term "voltage" in the shorthand sense, one must be clear about the two points between which the voltage is specified or measured. When using a voltmeter to measure voltage difference, one electrical lead of the voltmeter must be connected to the first point, one to the second point.

### Voltage between two stated points

A common use of the term "voltage" is in specifying how many volts are dropped across an electrical device (such as a resistor). In this case, the "voltage", or more accurately, the "voltage drop across the device", can usefully be understood as the difference between two measurements. The first measurement uses one electrical lead of the voltmeter on the first terminal of the device, with the other voltmeter lead connected to ground. The second measurement is similar, but with the first voltmeter lead on the second terminal of the device. The voltage drop is the difference between the two readings. In practice, the voltage drop across a device can be measured directly and safely using a voltmeter that is isolated from ground, provided that the maximum voltage capability of the voltmeter is not exceeded.

Two points in an electric circuit that are connected by an "ideal conductor," that is, a conductor without resistance and not within a changing magnetic field, have a voltage difference of zero. However, other pairs of points may also have a voltage difference of zero. If two such points are connected with a conductor, no current will flow through the connection.

The voltage between A and C is the sum of the voltage between A and B and the voltage between B and C. The various voltages in a circuit can be computed using Kirchhoff's circuit laws.

When talking about alternating current (AC) there is a difference between instantaneous voltage and average voltage. Instantaneous voltages can be added as for direct current (DC), but average voltages can be meaningfully added only when they apply to signals that all have the same frequency and phase.

## Useful formulas

### DC (Direct current) circuits

$V = I*R ; \mathrm{(Ohm's} \; \mathrm{Law)}$
P = IV = I2R = V2 / R
$V = \sqrt{PR}$

Where V = voltage difference (SI unit: volt), I = electric current (SI unit: ampere), R = resistance (SI unit: ohm), P = power (SI unit: watt).

### AC (Alternating current) circuits

$V = \frac{P}{I\;\cos\phi}$
$V = \frac{\sqrt{P\;Z}}{\sqrt{\cos\phi}} \!\$
$V = \frac{I\;R}{\cos\phi}$

Where V=voltage, I=current, R=resistance, P=true power, Z=impedance, φ=phase difference between I and V.

### AC conversions

$V_{avg} = 0.637\,V_{pk} = \frac{2}{\pi} V_{pk} = \frac{\omega}{\pi}\int_0^{\pi/\omega} V_{pk} \sin(\omega t - k x) {\rm{d}}x \!\$
$V_{rms} = 0.707\,V_{pk} = \frac{1}{\sqrt{2}} V_{pk} = V_{pk} \sqrt{\langle \sin^2(\omega t - k x) \rangle} \!\$
$V_{pk} = 0.5\,V_{ppk} \!\$
$V_{avg} = 0.319\,V_{ppk}\!\$
$V_{rms} = 0.354\,V_{ppk} = \frac{1}{2 \sqrt{2}} V_{ppk}\!\$
$V_{avg} = 0.900\,V_{rms} = \frac{2 \sqrt{2}}{\pi} V_{rms}\!\$

Where Vpk=peak voltage, Vppk=peak-to-peak voltage, Vavg=average voltage over a half-cycle, Vrms=effective (root mean square) voltage, and we assumed a sinusoidal wave of the form Vpksin(ωtkx), with a period T = 2π / ω, and where the angle brackets (in the root-mean-square equation) denote a time average over an entire period.

### Total voltage

Voltage sources and drops in series:

$V_T = V_1 + V_2 + V_3 + ... + V_n \!\$

Voltage sources and drops in parallel:

$V_T = V_1 = V_2 = V_3 = ... = V_n \!\$

Where $n \!\$ is the nth voltage source or drop

### Voltage drops

Across a resistor (Resistor R):

$V_R = IR_R \!\$

Across a capacitor (Capacitor C):

$V_C = IX_C \!\$

Across an inductor (Inductor L):

$V_L = IX_L \!\$

Where V=voltage, I=current, R=resistance, X=reactance.

## Measuring instruments

A multimeter set to measure voltage.

Instruments for measuring voltage differences include the voltmeter, the potentiometer, and the oscilloscope. The voltmeter works by measuring the current through a fixed resistor, which, according to Ohm's Law, is proportional to the voltage difference across the resistor. The potentiometer works by balancing the unknown voltage against a known voltage in a bridge circuit. The cathode-ray oscilloscope works by amplifying the voltage difference and using it to deflect an electron beam from a straight path, so that the deflection of the beam is proportional to the voltage difference.

## Safety

Voltages as low as 50 volts can lead to a lethal electric shock under certain circumstances. Electrical safety is discussed in the articles on high voltage and electric shock.

## References

1. ^ "To find the electric potential difference between two points A and B in an electric field, we move a test charge q0 from A to B, always keeping it in equilibrium, and we measure the work WAB that must be done by the agent moving the charge. The electric potential difference is defined from VB − VA = WAB/q0" Halliday, D. and Resnick, R. (1974). Fundamentals of Physics. New York: John Wiley & Sons. p. 465.
2. ^ Demetrius T. Paris and F. Kenneth Hurd, Basic Electromagnetic Theory, Mc Graw Hill, New York 1969, ISBN 0-48470-8 page 546
3. ^ Griffiths, D. (1999). Introduction to Electrodynamics. Upper Saddle River, NJ: Prentice-Hall.
4. ^ CollinsLanguage.com

.]]

The voltage between two points is a short name for the electrical force that would drive an electric current between those points. Specifically, voltage is equal to energy per unit charge.[1] In the case of static electric fields, the voltage between two points is equal to the electrical potential difference between those points. In the more general case with electric and magnetic fields that vary with time, the terms are no longer synonymous.[2]

Electric potential is the energy required to move a unit electric charge to a particular place in a static electric field.[3]

Voltage can be measured by a voltmeter. The unit of measurement is the volt.

## Definition

File:Opfindelsernes bog3
The electric field around the rod exerts a force on the charged pith ball, in an electroscope.
File:Electrostatic definition of
In a static field, the work is independent of the path.

The voltage between two ends of a path is the total energy required to move a small electric charge along that path, divided by the magnitude of the charge. Mathematically this is expressed as the line integral of the electric field and the time rate of change of magnetic field along that path. In the general case, both a static (unchanging) electric field and a dynamic (time-varying) electromagnetic field must be included in determining the voltage between two points.

Historically this quantity has also been called "tension"[4] and "pressure". Pressure is now obsolete but tension is still used, for example within the phrase "high tension" (HT) which is commonly used in thermionic valve (vacuum tube) based electronics.

## Hydraulic analogy

A simple analogy for an electric circuit is water flowing in a closed circuit of pipework, driven by a mechanical pump. This can be called a water circuit. Voltage difference between two points corresponds to the water pressure difference between two points. If there is a water pressure difference between two points, then water flow (due to the pump) from the first point to the second will be able to do work, such as driving a turbine. In a similar way, work can be done by the electric current driven by the voltage difference due to an electric battery: for example, the current generated by an automobile battery can drive the starter motor in an automobile. If the pump isn't working, it produces no pressure difference, and the turbine will not rotate. Equally, if the automobile's battery is flat, then it will not turn the starter motor.

This water flow analogy is a useful way of understanding several electrical concepts. In such a system, the work done to move water is equal to the pressure multiplied by the volume of water moved. Similarly, in an electrical circuit, the work done to move electrons or other charge-carriers is equal to "electrical pressure" (an old term for voltage) multiplied by the quantity of electrical charge moved. Voltage is a convenient way of measuring the ability to do work. In relation to "flow", the larger the "pressure difference" between two points (voltage difference or water pressure difference) the greater the flow between them (either electric current or water flow).

## Applications

Specifying a voltage measurement requires explicit or implicit specification of the points across which the voltage is measured. When using a voltmeter to measure voltage difference, one electrical lead of the voltmeter must be connected to the first point, one to the second point.

A common use of the term "voltage" is in describing the voltage dropped across an electrical device (such as a resistor). The voltage drop across the device can be understood as the difference between measurements at each terminal of the device with respect to a common reference point ( or ground). The voltage drop is the difference between the two readings. Two points in an electric circuit that are connected by an ideal conductor without resistance and not within a changing magnetic field, have a voltage difference of zero. Any two points with the same potential may be connected by a conductor and no current will flow beween them.

The voltage between A and C is the sum of the voltage between A and B and the voltage between B and C. The various voltages in a circuit can be computed using Kirchhoff's circuit laws.

When talking about alternating current (AC) there is a difference between instantaneous voltage and average voltage. Instantaneous voltages can be added for direct current (DC) and AC, but average voltages can be meaningfully added only when they apply to signals that all have the same frequency and phase.

## Measuring instruments

set to measure voltage.]]


Instruments for measuring voltage differences include the voltmeter, the potentiometer, and the oscilloscope. The voltmeter works by measuring the current through a fixed resistor, which, according to Ohm's Law, is proportional to the voltage difference across the resistor. The potentiometer works by balancing the unknown voltage against a known voltage in a bridge circuit. The cathode-ray oscilloscope works by amplifying the voltage difference and using it to deflect an electron beam from a straight path, so that the deflection of the beam is proportional to the voltage difference.

 Electronics portal

## References

1. ^ "To find the electric potential difference between two points A and B in an electric field, we move a test charge q0 from A to B, always keeping it in equilibrium, and we measure the work WAB that must be done by the agent moving the charge. The electric potential difference is defined from VB − VA = WAB/q0" Halliday, D. and Resnick, R. (1974). Fundamentals of Physics. New York: John Wiley & Sons. p. 465.
2. ^ Demetrius T. Paris and F. Kenneth Hurd, Basic Electromagnetic Theory, Mc Graw Hill, New York 1969, ISBN 0-48470-8 page 546
3. ^ Griffiths, D. (1999). Introduction to Electrodynamics. Upper Saddle River, NJ: Prentice-Hall.
4. ^ CollinsLanguage.com

# Study guide

Up to date as of January 14, 2010

### From Wikiversity

This lesson is designed to teach you some 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 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) and you have the picture.

   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 indeed. Good insulators include most pure plastics, wood, ceramic, glass, rubber and 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 the law (though I can't recall the name of that law off the top of my head).

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 are experience only the force, or electrical potential, of 3 volts. These bulbs do not light at all or shine very weakly indeed.

   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 he 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.

Shawn Daniel Hendricks 18:02, 26 May 2008 (UTC)

# Wikibooks

Up to date as of January 23, 2010
(Redirected to Electronics/DC Voltage and Current article)

### From Wikibooks, the open-content textbooks collection

Electronics | Foreword | Basic Electronics | Complex Electronics | Electricity | Machines | History of Electronics | Appendix | edit

## Ohm's Law

Ohm's law describes the relationship between voltage, current, and resistance.

Voltage and current are proportional at a given temperature:

$V = I \cdot R$

Voltage (V) is measured in volts (V); Current (I) in amperes (A); and resistance (R) in ohms (Ω).

In this example, the current going through any point in the circuit, I, will be equal to the voltage V divided by the resistance R.

In this example, the voltage across the resistor, V, will be equal to the supplied current, I, times the resistance R.

If two of the values (V, I, or R) are known, the other can be calculated using this formula.

Any more complicated circuit has an equivalent resistance that will allow us to calculate the current draw from the voltage source. Equivalent resistance is worked out using the fact that all resistor are either in parallel or series. Similarly, if the circuit only has a current source, the equivalent resistance can be used to calculate the voltage dropped across the current source.

## Kirchoff's Voltage Law

Kirchoff's Voltage Law (KVL): The sum of voltage drops around any loop in the circuit that starts and ends at the same place must be zero.

When you have a positive potential on one side of a battery, then there must be a negative potential on the other side of the battery.

(With Kirchoff's law, it's the sum of the voltages around the entire loop -- including the battery -- that equals zero. So, say you just have a 9 Volt battery connected to a resistor: there's 9V across the resistor, and 9V across the battery; the directions work out so that they subtract: 9V − 9V = 0.)

Analogy to elevation: A person is at the bottom of a mountain. They walk up the mountain, down the other side, and around to their starting position. Even though they changed elevation during the walk, they are at the same elevation as when they started.

### KVL Example

Insert diagram and example here: A voltage source and two resistors in series. Calculate the voltage across each component using ohm's law and the students knowledge of resistors in series, then start at ground, add the voltage source, and then subtract the drops across each resistor, and show that it comes back to zero.

## Voltage as a Physical Quantity

Voltage is the potential difference between two charged objects.

You really should put in something here about voltage being equal to the electric field times distance. It's the analogue equation of the gravitational potential of an object equalling the gravitational field times height.
Yeah. It should go in the Basic Concepts section, though. Analogies are always good.
Another way of thinking about voltage is potential energy per unit of charge. This gives a similar connection to gravitational potential -- to get the potential energy you multiply gravitational potential by mass or multiply the electrical potential by charge. In addition, it gives a connection to p=iv. Power is a change in energy divided by time. Voltage times current is the same as voltage*charge / time, which is energy divided by time.

The nice things about potentials is you can add or subtract them in series to make larger or smaller potentials as is commonly done in batteries.

Electrons flow from areas of high potential to lower potential.

At a given place in a circuit there are numerous paths to ground (what about negative voltages?). Each of them has the same voltage as they have the same potential from ground (why?) (-> because of KVL).

All the components of a circuit have resistance that acts as a potential drop.

Additional note: The following explains why voltage is "analogous" to the pressure of a fluid in a pipe (although, of course, it is only an analogy, not exactly same thing), and it also explains the strange-sounding "dimensions" of voltage. Consider the potential energy of compressed air being pumped into tank. The energy increases with each new increment of air. Pressure is that energy divided by the volume, which we can understand intuitively. Now consider the energy of electric charge (measured in coulombs) being forced into a capacitor. Voltage is that energy per charge, so voltage is analogous to a pressure-like sort of forcefulness. Also, dimensional analysis tells us that voltage ("energy per charge") divides out to be "charge per distance," the distance being between the plates of the capacitor. (More discussion is on page 16 of "Industrial Electronics," by D. J. Shanefield, Noyes Publications, Boston, 2001.)

## Kirchoff's Current Law

Kirchoff's Current Law (KCL): The sum of all current entering a node must equal the sum of all currents leaving the node.

Kirchoff's current law can be described with a sentence as "What comes in, must go out". It's that simple.

This means that current is conserved. If you have a current into a junction, the same current must go out of the junction.

Analogy to traffic: The number of cars entering an intersection is equal to the number of cars leaving the intersection.

### KCL Example

-I1 + I2 + I3 = 0 ↔ I1 = I2 + I3

I1 - I2 - I3 - I4 = 0 ↔ I2 + I3 + I4 = I1

$I_1 = I_2 + I_3 + \cdots + I_n \,\!$

Here is more about Kirchhoff's laws, which can be integrated here

## Consequences of KVL and KCL

#### Voltage Dividers

If two circuit elements are in series, there is a voltage drop across each element, but the current through both must be the same. The voltage at any point in the chain divides according to the resistances. A simple circuit with two (or more) resistors in series with a source is called a voltage divider.

Figure A: Voltage Divider circuit.

Consider the circuit in Figure A. According to KVL the voltage Vin is dropped across resistors R1 and R2. If a current i flows through the two series resistors then by Ohm's Law.

$i = \frac{V_{in}}{R_1+R_2}$.

So

$V_{out}=iR_2 \,\!$

Therefore

$V_{out}=\frac{V_{in}R_2}{R_1+R_2}$

Similary if VR1 is the voltage across R1 then

$V_{R1}=\frac{V_{in}R_1}{R_1+R_2}$

In general for n series resistors the voltage dropped across one of them say Ri is

$V_{Ri}=\frac{V_{in}R_i}{R_{eq}}$

Where

$R_{eq}=R_1+\cdots+R_n$
##### Voltage Dividers as References

Clearly voltage dividers can be used as references if you have a 9 volt battery and you want 4.5 volts then connect two equal valued resistors in series and take the reference across the second and ground. There are clearly other concerns though the first concern is current draw and the effect of the source impedance clearly connecting two 100 ohm resistors is a bad idea if the source impedance is say 50 ohms. Then the current draw would be 0.036 mA which is quite large if the battery is rated say 200 milliampere hours. The loading is more annoying with that source impedance too, the reference voltage with that source impedance is $\frac {9(100)}{250}=3.6\mbox{ V}$. So clearly increasing the order of the resistor to at least 1 kΩ is the way to go to reduce the current draw and the effect of loading. The other problem with these voltage divider references is that the reference cannot be loaded if we put a 100 Ω resistor in parallel with a 10 kΩ resistor, when the voltage divider is made of two 10 kΩ resistors, then the resistance of the reference resistor becomes somewhere near 100 Ω. This clearly means a terrible reference. If a 10 MΩ resistor is used for the reference resistor will still be some where around 10 kΩ but still probably less. The effect of tolerances is also a problem; if the resistors are rated 5% then the resistance of 10 kΩ resistors can vary by ±500 Ω. This means more inaccuracy with this sort of reference.

#### Current Dividers

If two elements are in parallel, the voltage across them must be the same, but the current divides according to the resistances. A simple circuit with two (or more) resistors in parallel with a source is called a current divider.

Figure B: Parallel Resistors.

If a voltage V appears across the resistors in Figure B with only R1 and R2 for the moment then the current flowing in the circuit, before the division, i is according to Ohms Law.

$i=\frac{V}{R_{eq}}$

Using the equivalent resistance for a parallel combination of resistors is

$i=\frac{V(R_1+R_2)}{R_1R_2}$ (1)

The current through R1 according to Ohms Law is

$i_1=\frac{V}{R_1}$ (2)

Dividing equation (2) by (1)

$i_1=\frac{iR_2}{R_2+R_1}$

Similarly

$i_2=\frac{iR_1}{R_2+R_1}$

In general with n Resistors the current ix is

$i_x=\frac{iR_1R_2\cdots R_n}{ (R_2\cdots R_n+\cdots+ R_1\cdots R_{n-1}) R_x}$

Or possibly more simply

$\frac{i_x}{i}=\frac{R_{eq}}{R_x}$

Where

$R_{eq}=\frac{R_1\cdots R_n}{R_2\cdots R_n+\cdots+ R_1\cdots R_{n-1}}$

# Simple English

Voltage is the change in electric potential (meaning potential energy per unit charge) between two positions.

If voltage is increased in a circuit then the overall charge in the circuit also increases. This is because the engery per unit is rising and therefore the entire energy will rise.

It is measured in volts. It was named after an Italian physicist Alessandro Volta who made the first chemical battery. Many other languages uses a word that means electric tension for voltage.

## Mathematical definition

Mathematically, the voltage is the amount of work needed to move a charge from one position to the other.

$V = I R$

Where V=Voltage, I=Current, R=Total resistance.

## Measuring tools

Some of the tools for measuring the voltage are the voltmeter and oscilloscope. The voltmeter measures the current going through a fixed resistor, then the voltage can be found using Ohm's law. The potentiometer works by balancing the unknown voltage against the known voltage inside a ring created by two wires. The oscilloscope first increases voltage, then the oscilloscope uses the voltage to make the path of electrons bent. Then it uses the idea that the change in direction and the voltage are proportional to find the voltage.