ELECTRICAL QUANTITIES - Lecture Notes.pdf

Voltage, Current and Resistance All materials are made up from atoms, and all atoms consist of protons, neutrons and electrons. Protons, have a positive electrical charge. Neutrons have no electrical charge while Electrons, have a negative electrical charge. Atoms are bound together by powerful for...

Voltage, Current and Resistance All materials are made up from atoms, and all atoms consist of protons, neutrons and electrons. Protons, have a positive electrical charge. Neutrons have no electrical charge while Electrons, have a negative electrical charge. Atoms are bound together by powerful forces of attraction existing between the atoms nucleus and the electrons in its outer shell. When these protons, neutrons and electrons are together within the atom they are happy and stable. However, if we separate them they exert a potential of attraction called a potential difference. If we create a circuit or conductor for the electrons to drift back to the protons the flow of electrons is called a current. The electrons do not flow freely through the circuit, the restriction to this flow is called resistance. Then all basic electrical or electronic circuit consists of three separate but very much related quantities, Voltage, ( v ), Current, ( i ) and Resistance, ( Ω ). Voltage Voltage, ( V ) is the potential energy of an electrical supply stored in the form of an electrical charge. Voltage can be thought of as the force that pushes electrons through a conductor and the greater the voltage the greater is its ability to "push" the electrons through a given circuit. As energy has the ability to do work this potential energy can be described as the work required in joules to move electrons in the form of an electrical current around a circuit from one point or node to another. The difference in voltage between any two nodes in a circuit is known as the Potential Difference, p.d. sometimes called Voltage Drop. The Potential difference between two points is measured in Volts with the circuit symbol V, or lowercase "v", although Energy, E lowercase "e" is sometimes used. Then the greater the voltage, the greater is the pressure (or pushing force) and the greater is the capacity to do work. Batteries or power supplies are mostly used to produce a steady D.C. (direct current) voltage source such as 6v, 12v, 24v etc in electronic circuits and systems. While A.C. (alternating current) voltage sources are available for domestic house and industrial power and lighting as well as power transmission. The mains voltage supply in the United Kingdom is currently 230 volts a.c. and 110 volts a.c. in the USA. voltage source usually given as a battery symbol Voltage Symbols Electrical Current Electrical Current, ( I ) is the movement or flow of electrical charge and is measured in Amperes, symbol i, for intensity). It is the continuous and uniform flow (called a drift) of electrons (the negative particles of an atom) around a circuit that are being "pushed" by the voltage source. In reality, electrons flow from the negative (-ve) terminal to the positive (+ve) terminal of the supply and for ease of circuit understanding conventional current flow assumes that the current flows from the positive to the negative terminal. Generally in circuit diagrams the flow of current through the circuit usually has an arrow associated with the symbol, I, or lowercase i to indicate the actual direction of the current flow. However, this arrow usually indicates the direction of conventional current flow and not necessarily the direction of the actual flow.Current is measured in Amps Electric Charge or Quantity of electricity (Q) Quantity of electricity (Q) refers to the electric charge available when a current (I) flows through a given point in a circuit for a period of t seconds. It is measured in coulombs. Therefore in a time of t seconds, the quantity of electricity (Q) passing through a given point of circuit is given by Q = It. Where I is the current in amperes. Example 1.1. Determine the quantity of electricity passing through a circuit if a current of 10A flows for 12secs. Q = It coulombs I = 10A t = 12secs Q = 10 x 12 = 120c. Resistance The Resistance, ( R ) of a circuit is its ability to resist or oppose the flow of current (electron flow) through itself making it necessary to apply a greater voltage to the electrical circuit to cause the current to flow again. Resistance is measured in Ohms, Greek symbol ( Ω, Omega ) with prefixes used to denote Kilo-ohms (kΩ = 103Ω) and Mega-ohms (MΩ = 106Ω). Resistance cannot be negative only positive. Resistor Symbols For very low values of resistance, for example milli-ohms, (mΩ´s) it is sometimes more easier to use the reciprocal of resistance (1/R) rather than resistance (R) itself. The reciprocal of resistance is called Conductance, symbol (G) and it is the ability of a conductor or device to conduct electricity. While high values of conductance implies a good conductor, low values of conductance implying a bad conductor. The unit of conductance is the Siemen, symbol (S). Again, using the water relationship, resistance is the diameter or the length of the pipe the water flows through. The smaller the diameter of the pipe the larger the resistance to the flow of water, and therefore the larger the resistance. Relationship between Voltage and Current in a circuit of constant resistance.  Unit of Quantity Symbol Abbreviation Measure Voltage V or E Volt V Current I Amp A Resistance R Ohms Ω Ohms Law The relationship between Voltage, Current and Resistance in any DC electrical circuit was firstly discovered by the German physicist Georg Ohm, (1787 - 1854). Georg Ohm found that, at a constant temperature, the electrical current flowing through a fixed linear resistance is directly proportional to the voltage applied across it, and also inversely proportional to the resistance. This relationship between the Voltage, Current and Resistance forms the bases of Ohms Law and is shown below. Ohms Law Relationship By knowing any two values of the Voltage, Current or Resistance quantities we can use Ohms Law to find the third missing value. Ohms Law is used extensively in electronics formulas and calculations so it is "very important to understand and accurately remember these formulas". To find the Voltage, ( V ) [V=IxR] V (volts) = I (amps) x R (Ω) To find the Current, ( I ) [I=V÷R] I (amps) = V (volts) ÷ R (Ω) To find the Resistance, ( R ) [R=V÷I] R (Ω) = V (volts) ÷ I (amps) Then by using Ohms Law we can see that a voltage of 1V applied to a resistor of 1Ω will cause a current of 1A to flow and the greater the resistance, the less current will flow for any applied voltage. Any Electrical device or component that obeys "Ohms Law" that is, the current flowing through it is proportional to the voltage across it (I α V), such as resistors or cables, are said to be "Ohmic" in nature, and devices that do not, such as transistors or diodes, are said to be "Non-ohmic" devices. Power in Electrical Circuits Electrical Power, (P) in a circuit is the amount of energy that is absorbed or produced within the circuit. A source of energy such as a voltage will produce or deliver power while the connected load absorbs it. The quantity symbol for power is P and is the product of voltage multiplied by the current with the unit of measurement being the Watt (W) with prefixes used to denote milliwatts (mW = 10-3W) or kilowatts (kW = 103W). By using Ohm's law and substituting for V, I and R the formula for electrical power can be found as: To find the Power (P) [P=VxI] P (watts) = V (volts) x I (amps) Also, [ P = V2 ÷ R ] P (watts) = V2 (volts) ÷ R (Ω) Also, [ P = I2 x R ] P (watts) = I2 (amps) x R (Ω) Again, the three quantities have been superimposed into a triangle this time called the Power Triangle with power at the top and current and voltage at the bottom. Again, this arrangement represents the actual position of each quantity in the Ohms law power formulas. One other point about Power, if the calculated power is positive in value for any formula the component absorbs the power, but if the calculated power is negative in value the component produces power, in other words it is a source of electrical energy. Also, we now know that the unit of power is the WATT but some electrical devices such as electric motors have a power rating in Horsepower or hp. The relationship between horsepower and watts is given as: 1hp = 746W.. For the circuit shown below find the Voltage (V), the Current (I), the Resistance (R) and the Power (P). Voltage [ V = I x R ] = 2 x 12Ω = 24V Current [ I = V ÷ R ] = 24 ÷ 12Ω = 2A Resistance [ R = V ÷ I ] = 24 ÷ 2 = 12 Ω Power [ P = V x I ] = 24 x 2 = 48W Power within an electrical circuit is only present when BOTH voltage and current are present for example, In an Open-circuit condition, Voltage is present but there is no current flow I = 0 (zero), therefore V x 0 is 0 so the power dissipated within the circuit must also be 0. Likewise, if we have a Short-circuit condition, current flow is present but there is no voltage V = 0, therefore 0 x I = 0 so again the power dissipated within the circuit is 0. As electrical power is the product of V x I, the power dissipated in a circuit is the same whether the circuit contains high voltage and low current or low voltage and high current flow. Generally, power is dissipated in the form of Heat (heaters), Mechanical Work such as motors, etc Energy in the form of radiated (Lamps) or as stored energy (Batteries). Energy in Electrical Circuits Electrical Energy that is either absorbed or produced is the product of the electrical power measured in Watts and the time in Seconds with the unit of energy given as Watt-seconds or Joules. Although electrical energy is measured in Joules it can become a very large value when used to calculate the energy consumed by a component. For example, a single 100 W light bulb connected for one hour will consume a total of 100 watts x 3600 sec = 360,000 Joules. So prefixes such as kilojoules (kJ = 103J) or megajoules (MJ = 106J) are used instead. If the electrical power is measured in "kilowatts" and the time is given in hours then the unit of energy is in kilowatt-hours or kWh which is commonly called a "Unit of Electricity" and is what consumers purchase from their electricity suppliers. Now that we know what is the relationship between voltage, current and resistance in a circuit, in the next tutorial about DC Theory we will look at the Standard Electrical Units used in electrical and electronic engineering to enable us to calculate these values and see that each value can be represented by either multiples or sub-multiples of the unit. Electrical Units of Measure The standard SI units used for the measurement of voltage, current and resistance are the Volt [ V ], Ampere [ A ] and Ohms [ Ω ] respectively. Sometimes in electrical or electronic circuits and systems it is necessary to use multiples or sub-multiples (fractions) of these standard units when the quantities being measured are very large or very small. The following table gives a list of some of the standard units used in electrical formulas and component values. Standard Electrical Units Measuring Parameter Symbol Description Unit Unit of Electrical Potential Voltage Volt V or E V=I×R Unit of Electrical Current Current Ampere I or i I=V÷R Unit of DC Resistance Resistance Ohm R or Ω R=V÷I Reciprocal of Resistance Conductance Siemen G or ℧ G=1÷R Unit of Capacitance Capacitance Farad C C=Q÷V Unit of Electrical Charge Charge Coulomb Q Q=C×V Unit of Inductance Inductance Henry L or H VL = -L(di/dt) Unit of Power Power Watts W P = V × I or I2 × R Unit of AC Resistance Impedance Ohm Z Z2 = R2 + X2  Unit of Frequency Frequency Hertz Hz ƒ=1÷T