Electrical Engineering

1. Electrical Engineering Exploring Engineering

2. Electrical Circuits • Electric charge and current • What’s a circuit? • Analogy with water flow • Resistance & Ohm’s Law • Series and parallel circuits • Kirchhoff’s Laws • Electric Power

3. Electrical Circuits The following quantities are measured in an electrical circuit*; • Current: Denoted by I and measured in Amperes (A) • Resistance: Denoted by R and measured in  Ohms ( Ω ) • Electrical Potential (Voltage): Denoted byV and measured in  volts (V) * The word circuit has the implication of “circle” built into it. That’s because the electrons forming the current have to be conserved and always need a continuous path. 

4. Electrical Circuits • Current Current is the movement of electrical charge - the flow of electrons through the electronic circuit. The direction of a current flow in a metal wire is from positive to negative (the opposite direction of electron flow). Current is measured in AMPERES (AMPS, A ). • Resistance Resistance causes an opposition to the flow of electricity in a circuit. It is used to control the amount of voltage and/or amperage in a circuit. It is measured in OHMS (Ω). • Voltage Voltage is the electrical force that causes current to flow in a circuit. It is measured in VOLTS .

5. Electrical Symbols Electronic components are classed into either being Passive or Active devices. • Passive Devices contribute no power to a circuit or system. In fact they may drain electrical power. Examples are resistors, light bulbs, electrical heaters. • Active Devices are capable of generating voltages or currents. Examples are batteries and other electrical current and voltage sources. • By using schematics symbols we can represent real-life devices.

6. Electrical Circuits

7. Electrical Circuits

8. Electrical Circuits

9. Electrical Circuits

10. Electrical Circuits Example: Part of a Car’s Electrical Diagram

11. Ohm’s Law The ratio of voltage to current is called the resistance, and if the ratio is constant over a wide range of voltages, the material is said to be an "ohmic" material. If the material can be characterized by such a resistance, then the current can be predicted from the relationship:

12. Kirchhoff’s Voltage Law • Kirchhoff’s Voltage Law is a form of the Conservation of Energy Law. • KVL states that the algebraic sum of the voltages around a closed path in a circuit is equal to zero. Σ V(closed loop) = Σ IR(closed loop) = 0

13. Kirchhoff’s Current Law • Kirchhoff’s Current Lawis a form of the Conservation of Charge Law. • KCL states that the algebraic sum of the currents in the branches that converge to any node is equal to zero Σ I(node) = 0

14. Series and Parallel Circuits Simple circuits are categorized in two types: • Series Circuits • Parallel Circuits For circuits with series and parallel sections, break the circuit up into portions of series and parallel, then calculate values for these portions, and use these values to calculate the resistance of the entire circuit. Or, for each individual series path, calculate the total resistance for that path. Second, using these values, by assuming that each path as a single resistor, calculate the total resistance of the circuit.

15. Resistors in Series • A series circuit is one with all the loads in a row, like links in a chain. There is only one path for the electricity to flow. • Add the resistances together to get the total resistance.

16. Resistors in Parallel • A parallel circuit is one that has two or more paths for the electricity to flow. In other words, the loads are parallel to each other. • Add the inverse of the resistances together to get the inverse of the total or equivalent resistance.

17. Example:  Find the currents in the following circuit. Solution: Assign currents to each part of the circuit between the node points. We have two node points that will give us three different currents. Assume that the currents move in a clockwise direction. The current on the segment EFAB is I1, on the segment BCDE is I3 and on the segment EB is I2.

18. Solution Continued • Using the  Kirchhoff's Current Law for the node  B yields the equation I1 + I2 - I3 = 0 • For the node E we will get the same equation. Then we use Kirchhoff's voltage law - 4×I1+ (-30) - 5×I1 - 10×I1 + 60 +10×I2 = 0 Or -19I1 + 10I2 = -30

19. Solution Continued • When we go through the battery from (-) to (+) on segment EF, potential difference is -30 V, and on segment FA moving through the resistor of 5W will result in the potential difference of -5*I1.  In a similar way we can find the potential differences on the other segment of the loop EFAB. • In the loop  BCDE, Kirchhoff's voltage law will yield the following equation: - 30×I3 + 120 - 10×I2 + 60 = 0 Or -10I2 – 30I3 = -180

20. Solution Continued • Now we have three equations with three unknowns: 1)  I1 + I2 - I3 = 02) - 19×I1  + 10×I2 = - 303) - 10×I2 – 30×I3 = -180 • This linear system can be solved by methods of simple algebra. The system above has the following solution: I1 = 2.8 AI2 = 2.4 AmpI3 = 5.2 Amp

21. Parallel Circuits • A parallel circuit is a circuit in which there are at least two independent paths in the circuit to get back to the source. In a parallel circuit, the current will flow through the closed paths and not through the open paths. • Consider a simple circuit with an outlet, a switch, and a 60-watt light bulb. If the switch is closed, the light operates. When a second 60-watt bulb is added to the circuit in parallel with the first bulb, it is connected so that there is a path to flow through to the first bulb or a path to flow through to the second bulb. Note that both bulbs glow at their intended brightness, since they each receive the full circuit voltage of 120 volts.

22. Parallel Circuits • Every load connected in a separate path receives the full circuit voltage. If a third 60-watt bulb is added to the circuit, it also glows as intended since it receives its full 120 volts. • One special concern in parallel circuits is that the amperage from the source increases each time another load is added to the circuit in parallel. Therefore, it is very easy to keep adding loads or plugging them in parallel and thereby overloading a circuit by requiring more current to flow than the circuit can safely handle. • An obvious advantage of parallel circuits is that the burnout or removal of one bulb does not affect the other bulbs in parallel circuits. They continue to operate because there is still a separate, independent closed path from the source to each of the other loads. That is why parallel circuits are used for wiring lighting and receptacle outlets. If one light on a parallel circuit burns out, it is the only one that quits and the other lights wired in parallel stay on.

23. Parallel Circuits • The following rules apply to a parallel circuit: • The potential drops of each branch equals the potential rise of the source. The total current is equal to the sum of the currents in the branches.

24. Parallel Circuits • The inverse of the total resistance of the circuit (also called effective resistance) is equal to the sum of the inverses of the individual resistances. • One important thing to notice from this last equation is that the more branches you add to a parallel circuit (the more things you plug in) the lower the total resistance becomes. Remember that as the total resistance decreases, the total current increases. So, the more things you plug in, the more current has to flow through the wiring in the wall. That's why plugging too many things in to one electrical outlet can create a real fire hazard.

25. DC Circuit Water Analogy • Each quantity in a battery-operated DC circuit has a direct analog in the water circuit. The nature of the analogies can help develop an understanding of the quantities in basic electric circuits. In the water circuit, the pressure P drives the water around the closed loop of pipe at a certain flow rate F. If the resistance to flow R is increased, then the flow rate decreases proportionately.

26. Current Law and Flow Rate

27. Current Law and Flow Rate For any circuit, fluid or electric, that has multiple branches and parallel elements, the flow rate through any cross-section must be the same. This is sometimes called the principle of continuity.

28. Voltage Law and Pressure

29. Voltage Law and Pressure

30. DC Electric Power • The electric power in watts associated with a complete electric circuit or a circuit component represents the rate at which energy is converted from the electrical energy of the moving charges to some other form, e.g., heat, mechanical energy, or energy stored in electric fields or magnetic fields. • For a resistor in a D C Circuit the product of voltage and electric current gives the power: P = V x I Power = Voltage x Current • The details of the units are as follows:

31. DC Electric Power • Convenient expressions for the power dissipated in a resistor can be obtained by the use of Ohm's Law. • The fact that the power dissipated in a given resistance depends upon the square of the current dictates that for high power applications you should minimize the current. This is the rationale for transforming power to very high voltages (and low currents) for cross-country electric power distribution.

32. Household Electricity Alternating current or AC electricity is the type of electricity commonly used in homes and businesses throughout the world. • The flow of electrons through a wire in direct current (DC) electricity is continuous in one direction, but the current in AC electricity alternates back and forth. • The back-and-forth motion occurs between 50 and 60 times per second, depending on the electrical system of the country. • What is special about AC electricity is that the voltage in can be readily changed (transformed to higher or lower values), thus making it more suitable for long-distance transmission than DC electricity.

33. AC Ohm's Law • AC means the driving voltage behaves sinusoidally and the corresponding alternating current may lead or lag it. • The alternating current analog to Ohm's law is where Z is the impedance of the circuit and V and I are the effective values (root mean square, or RMS) of the voltage and current.

34. House Wiring Diagram

35. Basic AC Circuits • AC circuits have a black “hot” or power wire, a white “neutral” or return wire and a green “ground” wire. • The ground wire protects you from getting shocked.

37. Formula Wheel If you have trouble remembering these formula, here is a useful tool.

38. Summary • Electricity is your friend • The governing laws include: • Conservation of electric charge (i.e., electrons) • Ohm’s Law, V = RI • Kirchhoff's laws of current an voltage • Power in a DC dissipative circuit is IV, I2R, or V2/R.