Ohm’s Law

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Battery Terminology

Words of caution:

Lead-acid batteries contain a diluted sulfuric acid electrolyte, which is a highly corrosive poison and will produce flammable and toxic gasses when recharged and explode if ignited. According to PREVENT BLINDNESS AMERICA, in 2003 nearly 6,000 motorists suffered serious eye injuries from working around car batteries. The U.S. Eye Injury Registry reports that it is the third leading cause of eye injuries at home. When working with batteries, you need to wear glasses (or preferably Z-87 rated safety goggles), have plenty of ventilation, remove your jewelry, and exercise caution. Do NOT allow battery electrolyte to mix with salt water. Even small quantities of this combination will produce chlorine gas that can KILL you! If available, please always follow the manufacturer's instructions for testing, jumping, installing, discharging, charging, equalizing and maintaining batteries.

A Glossary of Battery Terms

Ampere-Hour -- One ampere-hour is equal to a current of one ampere flowing for one hour. A unit-quantity of electricity used as a measure of the amount of electrical charge that may be obtained from a storage battery before it requires recharging.
Ampere-Hour Capacity -- The number of ampere-hours which can be delivered by a storage battery on a single discharge. The ampere-hour capacity of a battery on discharge is determined by a number of factors, of which the following are the most important: final limiting voltage; quantity of electrolyte; discharge rate; density of electrolyte; design of separators; temperature, age, and life history of the battery; and number, design, and dimensions of electrodes.
Anode -- In a primary or secondary cell, the metal electrode that gives up electrons to the load circuit and dissolves into the electrolyte.
Aqueous Batteries -- Batteries with water-based electrolytes.
Available Capacity -- The total battery capacity, usually expressed in ampere-hours or milliampere-hours that are available to perform work. This depends on factors such as the endpoint voltage, quantity and density of electrolyte, temperature, discharge rate, age, and the life history of the battery.
Battery -- A device that transforms chemical energy into electric energy. The term is usually applied to a group of two or more electric cells connected together electrically. In common usage, the term "battery" is also applied to a single cell, such as a household battery.
Battery Types -- There are, in general, two type of batteries: primary batteries, and secondary storage or accumulator batteries. Primary types, although sometimes consisting of the same active materials as secondary types, are constructed so that only one continuous or intermittent discharge can be obtained. Secondary types are constructed so that they may be recharged, following a partial or complete discharge, by the flow of direct current through them in a direction opposite to the current flow on discharge. By recharging after discharge, a higher state of oxidation is created at the positive plate or electrode and a lower state at the negative plate, returning the plates to approximately their original charged condition.
Battery Capacity -- The electric output of a cell or battery on a service test delivered before the cell reaches a specified final electrical condition and may be expressed in ampere-hours, watt-hours, or similar units. The capacity in watt-hours is equal to the capacity in ampere-hours multiplied by the battery voltage.
Battery Charger -- A device capable of supplying electrical energy to a battery.
Battery-Charging Rate -- The current expressed in amperes at which a storage battery is charged.
Battery Voltage, final -- The prescribed lower-limit voltage at which battery discharge is considered complete. The cutoff or final voltage is usually chosen so that the useful capacity of the battery is realized. The cutoff voltage varies with the type of battery, the rate of discharge, the temperature, and the kind of service in which the battery is used. The term "cutoff voltage" is applied more particularly to primary batteries, and "final voltage" to storage batteries. Synonym: Voltage, cutoff.
C -- The rated capacity, in ampere-hours, for a specific, constant discharge current (where i is the number of hours the cell can deliver this current). For example, the C₅ capacity is the ampere-hours that can be delivered by a cell at constant current in 5 hours. As a cell's capacity is not the same at all rates, C₅ is usually less than C₂₀ for the same cell.
Capacity -- The quantity of electricity delivered by a battery under specified conditions, usually expressed in ampere-hours.
Cathode -- In a primary or secondary cell, the electrode that, in effect, oxidizes the anode or absorbs the electrons.
Cell -- An electrochemical device, composed of positive and negative plates, separator, and electrolyte, which is capable of storing electrical energy. When encased in a container and fitted with terminals, it is the basic "building block" of a battery.
Charge -- Applied to a storage battery, the conversion of electric energy into chemical energy within the cell or battery. This restoration of the active materials is accomplished by maintaining a unidirectional current in the cell or battery in the opposite direction to that during discharge; a cell or battery which is said to be charged is understood to be fully charged.
Charge Rate -- The current applied to a secondary cell to restore its capacity. This rate is commonly expressed as a multiple of the rated capacity of the cell. For example, the C/10 charge rate of a 500 Ah cell is expressed as,
C/10 rate = 500 Ah / 10 h = 50 A.
Charge, state of -- Condition of a cell in terms of the capacity remaining in the cell.
Charging -- The process of supplying electrical energy for conversion to stored chemical energy.
Constant-Current Charge -- A charging process in which the current of a storage battery is maintained at a constant value. For some types of lead-acid batteries this may involve two rates called the starting and finishing rates.
Constant-Voltage Charge -- A charging process in which the voltage of a storage battery at the terminals of the battery is held at a constant value.
Cycle -- One sequence of charge and discharge. Deep cycling requires that all the energy to an end voltage established for each system be drained from the cell or battery on each discharge. In shallow cycling, the energy is partially drained on each discharge; i.e., the energy may be any value up to 50%.
Cycle Life -- For secondary rechargeable cells or batteries, the total number of charge/discharge cycles the cell can sustain before it becomes inoperative. In practice, end of life is usually considered to be reached when the cell or battery delivers approximately 80% of rated ampere-hour capacity.
Depth of Discharge -- The relative amount of energy withdrawn from a battery relative to how much could be withdrawn if the battery were discharged until exhausted.
Discharge -- The conversion of the chemical energy of the battery into electric energy.
Discharge, deep -- Withdrawal of all electrical energy to the end-point voltage before the cell or battery is recharged.
Discharge, high-rate -- Withdrawal of large currents for short intervals of time, usually at a rate that would completely discharge a cell or battery in less than one hour.
Discharge, low-rate -- Withdrawal of small currents for long periods of time, usually longer than one hour.
Drain -- Withdrawal of current from a cell.
Dry Cell -- A primary cell in which the electrolyte is absorbed in a porous medium, or is otherwise restrained from flowing. Common practice limits the term "dry cell" to the Leclanch" cell, which is the common commercial type.
Electrochemical Couple -- The system of active materials within a cell that provides electrical energy storage through an electrochemical reaction.
Electrode -- An electrical conductor through which an electric current enters or leaves a conducting medium, whether it be an electrolytic solution, solid, molten mass, gas, or vacuum. For electrolytic solutions, many solids, and molten masses, an electrode is an electrical conductor at the surface of which a change occurs from conduction by electrons to conduction by ions. For gases and vacuum, the electrodes merely serve to conduct electricity to and from the medium.
Electrolyte -- A chemical compound which, when fused or dissolved in certain solvents, usually water, will conduct an electric current. All electrolytes in the fused state or in solution give rise to ions which conduct the electric current.
Electropositivity -- The degree to which an element in a galvanic cell will function as the positive element of the cell. An element with a large electropositivity will oxidize faster than an element with a smaller electropositivity.
End-of-Discharge Voltage -- The voltage of the battery at termination of a discharge.
Energy -- Output capability; expressed as capacity times voltage, or watt-hours.
Energy Density -- Ratio of cell energy to weight or volume (watt-hours per pound, or watt-hours per cubic inch).
Float Charging -- Method of recharging in which a secondary cell is continuously connected to a constant-voltage supply that maintains the cell in fully charged condition.
Galvanic Cell -- A combination of electrodes, separated by electrolyte, that is capable of producing electrical energy by electrochemical action.
Gassing -- The evolution of gas from one or both of the electrodes in a cell. Gassing commonly results from self-discharge or from the electrolysis of water in the electrolyte during charging.
Internal Resistance -- The resistance to the flow of an electric current within the cell or battery.
Memory Effect -- A phenomenon in which a cell, operated in successive cycles to the same, but less than full, depth of discharge, temporarily loses the remainder of its capacity at normal voltage levels (usually applies only to Ni-Cd cells).
Negative Terminal -- The terminal of a battery from which electrons flow in the external circuit when the cell discharges.
Nonaqueous Batteries -- Cells that do not contain water, such as those with molten salts or organic electrolytes.
Ohm's Law -- The formula that describes the amount of current flowing through a circuit. Voltage = Current " Resistance.
Open Circuit -- Condition of a battery which is neither on charge nor on discharge (i.e., disconnected from a circuit).
Open-Circuit Voltage -- The difference in potential between the terminals of a cell when the circuit is open (i.e., a no-load condition).
Oxidation -- A chemical reaction that results in the release of electrons by an electrode's active material.
Parallel Connection -- The arrangement of cells in a battery made by connecting all positive terminals together and all negative terminals together, the voltage of the group being only that of one cell and the current drain through the battery being divided among the several cells. See Series Connection.
Polarity -- Refers to the charges residing at the terminals of a battery.
Positive Terminal -- The terminal of a battery toward which electrons flow through the external circuit when the cell discharges.
Primary Battery -- A battery made up of primary cells. See Primary Cell.
Primary Cell -- A cell designed to produce electric current through an electrochemical reaction that is not efficiently reversible. Hence the cell, when discharged, cannot be efficiently recharged by an electric current. Note: When the available energy drops to zero, the cell is usually discarded. Primary cells may be further classified by the types of electrolyte used.
Rated Capacity -- The number of ampere-hours a cell can deliver under specific conditions (rate of discharge, end voltage, temperature); usually the manufacturer's rating.
Rechargeable -- Capable of being recharged; refers to secondary cells or batteries.
Recombination -- State in which the gasses normally formed within the battery cell during its operation, are recombined to form water.
Reduction -- A chemical process that results in the acceptance of electrons by an electrode's active material.
Seal -- The structural part of a galvanic cell that restricts the escape of solvent or electrolyte from the cell and limits the ingress of air into the cell (the air may dry out the electrolyte or interfere with the chemical reactions).
Secondary Battery -- A battery made up of secondary cells. See Storage Battery; Storage Cell.
Self Discharge -- Discharge that takes place while the battery is in an open-circuit condition.
Separator -- The permeable membrane that allows the passage of ions, but prevents electrical contact between the anode and the cathode.
Series Connection -- The arrangement of cells in a battery configured by connecting the positive terminal of each successive cell to the negative terminal of the next adjacent cell so that their voltages are cumulative. See Parallel Connection.
Shelf Life -- For a dry cell, the period of time (measured from date of manufacture), at a storage temperature of 21"C (69"F), after which the cell retains a specified percentage (usually 90%) of its original energy content.
Short-Circuit Current -- That current delivered when a cell is short-circuited (i.e., the positive and negative terminals are directly connected with a low-resistance conductor).
Starting-Lighting-Ignition (SLI) Battery -- A battery designed to start internal combustion engines and to power the electrical systems in automobiles when the engine is not running. SLI batteries can be used in emergency lighting situations.
Stationary Battery -- A secondary battery designed for use in a fixed location.
Storage Battery -- An assembly of identical cells in which the electrochemical action is reversible so that the battery may be recharged by passing a current through the cells in the opposite direction to that of discharge. While many non-storage batteries have a reversible process, only those that are economically rechargeable are classified as storage batteries. Synonym: Accumulator; Secondary Battery. See Secondary Cell.
Storage Cell -- An electrolytic cell for the generation of electric energy in which the cell after being discharged may be restored to a charged condition by an electric current flowing in a direction opposite the flow of current when the cell discharges. Synonym: Secondary Cell. See Storage Battery.
Taper Charge -- A charge regime delivering moderately high-rate charging current when the battery is at a low state of charge and tapering the current to lower rates as the battery becomes more fully charged.
Terminals -- The parts of a battery to which the external electric circuit is connected.
Thermal Runaway -- A condition whereby a cell on charge or discharge will destroy itself through internal heat generation caused by high overcharge or high rate of discharge or other abusive conditions.
Trickle Charging -- A method of recharging in which a secondary cell is either continuously or intermittently connected to a constant-current supply that maintains the cell in fully charged condition.
Vent -- A normally sealed mechanism that allows for the controlled escape of gases from within a cell.
Voltage, cutoff -- Voltage at the end of useful discharge. (See Voltage, end-point.)
Voltage, end-point -- Cell voltage below which the connected equipment will not operate or below which operation is not recommended.
Voltage, nominal -- Voltage of a fully charged cell when delivering rated current.
Wet Cell -- A cell, the electrolyte of which is in liquid form and free to flow and move.

Marine Wire

by Allied Wire & Cable, Inc.

The marine environment is a hostile one for electrical wire. Wire used on board a marine vessel will potentially be exposed to numerous obstacles, such as salt water, sunlight, heat and other outside hindrances. All electrical wires are not constructed to endure the problems associated with marine conditions and therefore will not be suitable wiring on boats or ships. In these situations, marine wire or boat cable may be necessary.

Marine wire, boat cable, and marine primary wire are terms you may have heard used in reference to electrical wiring for boats or marine vessels. Wiring specified as "marine" or "boat" is different in several ways from other types of electrical wire, such as power wire used in the home, or automotive wire, etc. A main difference is that the conditions surrounding marine installations require marine wire and boat cable to perform better than other wires designed chiefly for land use.

A marine wire is specifically designed and engineered for the electrical wiring of boats and is intended for all possible uses abroad a ship. Marine wire may be distributed to the pleasure boat and commercial marine industries and is often used by boat builders. The term "boat cable" may often be used interchangeably with marine wire or marine cable. Boat cable usually refers to general electrical wiring used on a boat. Marine wire that may fall into the sweeping category of "boat cable" often starts as a single conductor cable. Extra wires are added from there into one cable, consequently creating multi conductor boat cable.

Because of the demanding marine environment, approved marine wire usually possesses a copper conductor. In addition, the jacket of the cable will most likely have been tested for flammability safety. The jacket and the insulation should be rated water resistant.

The most frequently requested single conductor boat cable styles are marine primary wire and marine battery cable. The cables are extremely similar. The main factor that differentiates the two is the AWG size of the cable. According to General Isles Marine, single conductor boat cable in sizes 16 AWG up to 8 AWG are widely known as primary wire sizes. The larger single conductor marine cables ranging from size 6 AWG up to 4/0 AWG are known as battery cable sizes.

Often times, marine wire and boat cable provided by a manufacturer or distributor will meet the requirements of UL, SAE, Coast Guard, ABYC, and NMMA. The American Boat and Yacht Council (ABYC), the United States Coast Guard (USCG), the National Marine Manufacturers Association (NMMA) and the Society of Automotive Engineers (SAE) have developed safety standards and guidelines for marine electrical installations specifically serving manufacturers, technicians, and even boat owners.

Corrosion is a primary cause of electrical failures on a boat. In order to avoid the common problem, marine wire and boat cable are built to resist quick decay. In both wet and dry conditions, marine wire needs to behave consistently in order to perform properly. Marine wire, boat cable and marine primary wire may possess PVC insulation for added defense against the elements. After all, they need all of the help they can get.

The remaining links will examine the various types of marine wire and boat cable on the market today.

Common Types of Marine Wire

Marine Primary Wire (Tinned Copper)

Marine Primary Wire may also be listed as Tinned Primary Wire. The copper conductor will usually possess a tin coating which causes the strand to be called "tinned copper." Tinned copper marine primary wire is built to reduce corrosion and prevent electrical failure.

Marine Primary Wire (Tinned Copper) can be used in 105"C marine applications, in the internal wiring of electrical equipment and for general circuit wiring. It is employed for electrical connections in the marine and automotive environments where a tinned conductor is preferred. The marine primary wire may additionally be utilized for motorcycles and other applications requiring a high temperature primary wire. Tinned copper marine wire performs well in all marine environments, even in saltwater.

You may see marine primary wire listed as UL 1426 marine grade wire. Most brands of tinned primary wire will meet the requirements of the US Coast Guard and ABYC, as well as others.

Marine Primary Wire (Bare Copper)

Marine Primary Wire (Bare Copper) can be used in 105"C marine applications, in internal wiring of electrical equipment and for general circuit wiring. The marine primary wire shares many of the same applications and properties as tinned primary wire. However, the conductor is bare copper instead of tinned copper.

SAE Primary Wire

SAE Primary Wire is General Purpose Thermoplastic (GPT) insulated primary wire that corresponds to SAE specifications, generally specifications J1128 and J378. SAE Primary Wire may be used for general purpose marine and automotive applications. It usually has a temperature range of -20"C to 105"C and voltage rating of 50 volts.

Flat Boat Cable

Flat Boat Cable is a multi-conductor marine cable that can be used for marine or brake cable. The boat cable usually meets UL Standard 1426 and UL Style BC-5W2. Flat boat cable also may meet DOT Coast Guard specs. The boat cable has a PVC insulated multi-conductor.

Round Boat Cable

Round Boat Cable is much like flat boat cable. However, round boat cable makes for easy installation where tight, jagged spaces are present. Many installers of boat cable favor round cables because they are easier to arrange. Additionally, round boat cable may be used for harsh environments.

Marine Battery Cable

Marine Battery Cable generally has a temperature range of -20"C to 105"C and a voltage rating of 50 volts. The battery cable also resists oil, fuel and acid. Marine battery cable is designed to survive the harsh marine environments. The cable normally has a high strand count cable with tin plated copper stranding. Marine battery cable may be used in battery installations.

Nanobots

Nanobots are full-time employees of Ancor Wire who move copper to those areas of a boat’s marine electrical system that most require it.

Employed in a process called Nanotechnological Overload Sensing Heat Induced Tranference, the nanobots work to allow a boat wiring harness to move copper according to the power demands of attached accessories. This feature is currently found exclusively in Nanotech Brand Wire.

Because of limited production, this clever boat wiring product is only available one day each year.

An electric circuit is formed when a conductive path is created to allow free electrons to continuously move. This continuous movement of free electrons through the conductors of a circuit is called a current, and it is often referred to in terms of "flow," just like the flow of a liquid through a hollow pipe.

The force motivating electrons to "flow" in a circuit is called voltage. Voltage is a specific measure of potential energy that is always relative between two points. When we speak of a certain amount of voltage being present in a circuit, we are referring to the measurement of how much potential energy exists to move electrons from one particular point in that circuit to another particular point. Without reference to two particular points, the term "voltage" has no meaning.

Free electrons tend to move through conductors with some degree of friction, or opposition to motion. This opposition to motion is more properly called resistance. The amount of current in a circuit depends on the amount of voltage available to motivate the electrons, and also the amount of resistance in the circuit to oppose electron flow. Just like voltage, resistance is a quantity relative between two points. For this reason, the quantities of voltage and resistance are often stated as being "between" or "across" two points in a circuit.

To be able to make meaningful statements about these quantities in circuits, we need to be able to describe their quantities in the same way that we might quantify mass, temperature, volume, length, or any other kind of physical quantity. For mass we might use the units of "kilogram" or "gram." For temperature we might use degrees Fahrenheit or degrees Celsius. Here are the standard units of measurement for electrical current, voltage, and resistance:

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The "symbol" given for each quantity is the standard alphabetical letter used to represent that quantity in an algebraic equation. Standardized letters like these are common in the disciplines of physics and engineering, and are internationally recognized. The "unit abbreviation" for each quantity represents the alphabetical symbol used as a shorthand notation for its particular unit of measurement. And, yes, that strange-looking "horseshoe" symbol is the capital Greek letter Ω, just a character in a foreign alphabet (apologies to any Greek readers here).

Each unit of measurement is named after a famous experimenter in electricity: The amp after the Frenchman Andre M. Ampere, the volt after the Italian Alessandro Volta, and the ohm after the German Georg Simon Ohm.

The mathematical symbol for each quantity is meaningful as well. The "R" for resistance and the "V" for voltage are both self-explanatory, whereas "I" for current seems a bit weird. The "I" is thought to have been meant to represent "Intensity" (of electron flow), and the other symbol for voltage, "E," stands for "Electromotive force." From what research I've been able to do, there seems to be some dispute over the meaning of "I." The symbols "E" and "V" are interchangeable for the most part, although some texts reserve "E" to represent voltage across a source (such as a battery or generator) and "V" to represent voltage across anything else.

All of these symbols are expressed using capital letters, except in cases where a quantity (especially voltage or current) is described in terms of a brief period of time (called an "instantaneous" value). For example, the voltage of a battery, which is stable over a long period of time, will be symbolized with a capital letter "E," while the voltage peak of a lightning strike at the very instant it hits a power line would most likely be symbolized with a lower-case letter "e" (or lower-case "v") to designate that value as being at a single moment in time. This same lower-case convention holds true for current as well, the lower-case letter "i" representing current at some instant in time. Most direct-current (DC) measurements, however, being stable over time, will be symbolized with capital letters.

One foundational unit of electrical measurement, often taught in the beginnings of electronics courses but used infrequently afterwards, is the unit of the coulomb, which is a measure of electric charge proportional to the number of electrons in an imbalanced state. One coulomb of charge is equal to 6,250,000,000,000,000,000 electrons. The symbol for electric charge quantity is the capital letter "Q," with the unit of coulombs abbreviated by the capital letter "C." It so happens that the unit for electron flow, the amp, is equal to 1 coulomb of electrons passing by a given point in a circuit in 1 second of time. Cast in these terms, current is the rate of electric charge motion through a conductor.

As stated before, voltage is the measure of potential energy per unit charge available to motivate electrons from one point to another. Before we can precisely define what a "volt" is, we must understand how to measure this quantity we call "potential energy." The general metric unit for energy of any kind is the joule, equal to the amount of work performed by a force of 1 newton exerted through a motion of 1 meter (in the same direction). In British units, this is slightly less than 3/4 pound of force exerted over a distance of 1 foot. Put in common terms, it takes about 1 joule of energy to lift a 3/4 pound weight 1 foot off the ground, or to drag something a distance of 1 foot using a parallel pulling force of 3/4 pound. Defined in these scientific terms, 1 volt is equal to 1 joule of electric potential energy per (divided by) 1 coulomb of charge. Thus, a 9 volt battery releases 9 joules of energy for every coulomb of electrons moved through a circuit.

These units and symbols for electrical quantities will become very important to know as we begin to explore the relationships between them in circuits. The first, and perhaps most important, relationship between current, voltage, and resistance is called Ohm's Law, discovered by Georg Simon Ohm and published in his 1827 paper, The Galvanic Circuit Investigated Mathematically. Ohm's principal discovery was that the amount of electric current through a metal conductor in a circuit is directly proportional to the voltage impressed across it, for any given temperature. Ohm expressed his discovery in the form of a simple equation, describing how voltage, current, and resistance interrelate:

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In this algebraic expression, voltage (E) is equal to current (I) multiplied by resistance (R). Using algebra techniques, we can manipulate this equation into two variations, solving for I and for R, respectively:

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Let's see how these equations might work to help us analyze simple circuits:

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In the above circuit, there is only one source of voltage (the battery, on the left) and only one source of resistance to current (the lamp, on the right). This makes it very easy to apply Ohm's Law. If we know the values of any two of the three quantities (voltage, current, and resistance) in this circuit, we can use Ohm's Law to determine the third.

In this first example, we will calculate the amount of current (I) in a circuit, given values of voltage (E) and resistance (R):

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What is the amount of current (I) in this circuit?

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In this second example, we will calculate the amount of resistance (R) in a circuit, given values of voltage (E) and current (I):

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What is the amount of resistance (R) offered by the lamp?

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In the last example, we will calculate the amount of voltage supplied by a battery, given values of current (I) and resistance (R):

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What is the amount of voltage provided by the battery?

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Ohm's Law is a very simple and useful tool for analyzing electric circuits. It is used so often in the study of electricity and electronics that it needs to be committed to memory by the serious student. For those who are not yet comfortable with algebra, there's a trick to remembering how to solve for any one quantity, given the other two. First, arrange the letters E, I, and R in a triangle like this:

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If you know E and I, and wish to determine R, just eliminate R from the picture and see what's left:

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If you know E and R, and wish to determine I, eliminate I and see what's left:

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Lastly, if you know I and R, and wish to determine E, eliminate E and see what's left:

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Eventually, you'll have to be familiar with algebra to seriously study electricity and electronics, but this tip can make your first calculations a little easier to remember. If you are comfortable with algebra, all you need to do is commit E=IR to memory and derive the other two formulae from that when you need them!

REVIEW:

Voltage measured in volts, symbolized by the letters "E" or "V".
Current measured in amps, symbolized by the letter "I".
Resistance measured in ohms, symbolized by the letter "R".
Ohm's Law: E = IR ; I = E/R ; R = E/I

Published under the terms and conditions of the Design Science License

Power in Electric Circuits

In addition to voltage and current, there is another measure of free electron activity in a circuit: power. First, we need to understand just what power is before we analyze it in any circuits.

Power is a measure of how much work can be performed in a given amount of time. Work is generally defined in terms of the lifting of a weight against the pull of gravity. The heavier the weight and/or the higher it is lifted, the more work has been done. Power is a measure of how rapidly a standard amount of work is done.

For American automobiles, engine power is rated in a unit called "horsepower," invented initially as a way for steam engine manufacturers to quantify the working ability of their machines in terms of the most common power source of their day: horses. One horsepower is defined in British units as 550 ft-lbs of work per second of time. The power of a car's engine won't indicate how tall of a hill it can climb or how much weight it can tow, but it will indicate how fast it can climb a specific hill or tow a specific weight.

The power of a mechanical engine is a function of both the engine's speed and it's torque provided at the output shaft. Speed of an engine's output shaft is measured in revolutions per minute, or RPM. Torque is the amount of twisting force produced by the engine, and it is usually measured in pound-feet, or lb-ft (not to be confused with foot-pounds or ft-lbs, which is the unit for work). Neither speed nor torque alone is a measure of an engine's power.

A 100 horsepower diesel tractor engine will turn relatively slowly, but provide great amounts of torque. A 100 horsepower motorcycle engine will turn very fast, but provide relatively little torque. Both will produce 100 horsepower, but at different speeds and different torques. The equation for shaft horsepower is simple:

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Notice how there are only two variable terms on the right-hand side of the equation, S and T. All the other terms on that side are constant: 2, pi, and 33,000 are all constants (they do not change in value). The horsepower varies only with changes in speed and torque, nothing else. We can re-write the equation to show this relationship:

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Because the unit of the "horsepower" doesn't coincide exactly with speed in revolutions per minute multiplied by torque in pound-feet, we can't say that horsepower equals ST. However, they are proportional to one another. As the mathematical product of ST changes, the value for horsepower will change by the same proportion.

In electric circuits, power is a function of both voltage and current. Not surprisingly, this relationship bears striking resemblance to the "proportional" horsepower formula above:

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In this case, however, power (P) is exactly equal to current (I) multiplied by voltage (E), rather than merely being proportional to IE. When using this formula, the unit of measurement for power is the watt, abbreviated with the letter "W."

It must be understood that neither voltage nor current by themselves constitute power. Rather, power is the combination of both voltage and current in a circuit. Remember that voltage is the specific work (or potential energy) per unit charge, while current is the rate at which electric charges move through a conductor. Voltage (specific work) is analogous to the work done in lifting a weight against the pull of gravity. Current (rate) is analogous to the speed at which that weight is lifted. Together as a product (multiplication), voltage (work) and current (rate) constitute power.

Just as in the case of the diesel tractor engine and the motorcycle engine, a circuit with high voltage and low current may be dissipating the same amount of power as a circuit with low voltage and high current. Neither the amount of voltage alone nor the amount of current alone indicates the amount of power in an electric circuit.

In an open circuit, where voltage is present between the terminals of the source and there is zero current, there is zero power dissipated, no matter how great that voltage may be. Since P=IE and I=0 and anything multiplied by zero is zero, the power dissipated in any open circuit must be zero. Likewise, if we were to have a short circuit constructed of a loop of superconducting wire (absolutely zero resistance), we could have a condition of current in the loop with zero voltage, and likewise no power would be dissipated. Since P=IE and E=0 and anything multiplied by zero is zero, the power dissipated in a superconducting loop must be zero. (We'll be exploring the topic of superconductivity in a later chapter).

Whether we measure power in the unit of "horsepower" or the unit of "watt," we're still talking about the same thing: how much work can be done in a given amount of time. The two units are not numerically equal, but they express the same kind of thing. In fact, European automobile manufacturers typically advertise their engine power in terms of kilowatts (kW), or thousands of watts, instead of horsepower! These two units of power are related to each other by a simple conversion formula:

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So, our 100 horsepower diesel and motorcycle engines could also be rated as "74570 watt" engines, or more properly, as "74.57 kilowatt" engines. In European engineering specifications, this rating would be the norm rather than the exception.

REVIEW:

Power is the measure of how much work can be done in a given amount of time.
Mechanical power is commonly measured (in America) in "horsepower."
Electrical power is almost always measured in "watts," and it can be calculated by the formula P = IE.
Electrical power is a product of both voltage and current, not either one separately.
Horsepower and watts are merely two different units for describing the same kind of physical measurement, with 1 horsepower equaling 745.7 watts.

Published under the terms and conditions of the Design Science License