INTRODUCTION TO ELECTRICAL & ELECTRONIC ENGINEERING HOMEWORK ASSIGNMENT #1

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1 ENGG 1015 THE UNIVESITY OF HONG KONG HW#1 Edmund Y. Lam 1 st Semester 11/1 Kenneth K. Y. Wong INTODUCTION TO ELECTICAL & ELECTONIC ENGINEEING HOMEWOK ASSIGNMENT #1 Suggested Solution 1. Analog vs. Digital (a) Most naturally occurring quantities are continuous in nature. Here are some examples: height of a person velocity mass time length power force area (b) Some examples of naturally occurring discrete quantities: Human population number of fingers quantum states electron spin. Top-down vs. Bottom-up (a) Item Driven by system requement Driven by component integration Construct system by composing smaller parts Construct system by decomposing Generate new ideas from system requements Synthesize new ideas from existing components Must work with unknown system components as black-boxes Top-down Bottom-up (b) One example of top-down approach of making a ube Goldberg Machine: Decide the types of stages according to the location, number of stages, and interface of each stage Design stages according to the types of stages, input and output requements Find out the requed components for each stage Get all things ready (e.g. acque from the TA and technician)

2 Prepare and assemble each stage Combine each stage together Fine-tune the connection between stages One example of bottom-up approach of making a ube Goldberg Machine: Find out the components available Mix and match available components as different stages to meet the project requements such as types of stages according to the location, number of stages, and interface of each stage etc. Prepare and assemble each stage by the given equipments Combine each stage together Fine-tune the connection between stages 3. Ccuit Analysis 1 Measuring esistance by Balanced Ccuit (a) When i g is zero, that is, when the bridge is balanced, KCL reques that i1 = i i = i 3 x Now, because i g is zero, there is no voltage drop across DB, and therefore points D and B are at the same potential. Thus when the bridge is balanced, KVL reques that i 1 1= i 3 3 i = i x x with some substitutions: 3 x = 1 (b) If the ratio of 3 / 1 is known, the value of x can be calculated by adjusting the variable resistor until there is no current in V G. (c) 0 to 100 Ω (d) The ratio of 3 / 1 can be varied from 0 to 10,000 in decimal steps. However, note that the equation implies that x can vary from zero to infinity; the practical range of x is approximately 1 Ω to 1 MΩ. Lower resistances are difficult to measure on a standard Wheatstone bridge (as shown in Fig. 1) because of thermoelectric voltages generated at the junctions of dissimilar metals (i.e. as illustrated in Q4) and because of thermal heating effects that is, i effects. Higher resistances are difficult to measure accurately because of leakage currents. In other words, if x is large, the current leakage in the electrical insulation may be comparable to the current in the branches of the bridge ccuit. 4. Ccuit Analysis Temperature Sensor by Current Divider (a) By i = 0 [1 + α 0 (T 0)] Iron at 0 C, α i0 = , i0 = 8.5 Ω; Brass at 0 C, α b0=0.00-1, b0 = 10 Ω Therefore, at T C, it = bt

3 i0 [1 + α i0 (T 0)]= b0 [1 + α b0 (T 0)] 8.5 [ (T 0)]= 10[ (T 0)].675 x 10-3 T = T = C The temperature of the wes = C (b) Calculate the resistance of the wes at that temperature in (a). The resistance of on we = 8.5[ ( )] = 11.1 Ω The resistance of brass we = 10[ ( )] = 11.1 Ω (c) The current flowing through each we = 9 / 11.1 = 0.81A Power output from the voltage source = 9 * (9 / 11.1 * ) = W The sum of all power dissipated at the wes = (9 / 11.1) * 11.1 * = W Therefore, the power generated from the power source entely is dissipated as heat in the the two wes. (d) 9V o = 10Ω= ( Ti 0) Ti 5.1 C 0.9A + = 9V o = 11.5Ω= ( Tb 0) Tb = 6.5 C 0.8A (e) Connect the two pieces of metal in series instead. Then measure the voltages instead of currents as before. 5. QTI Optical Sensor (a) There is not enough current to turn on the lamp. (b) V V V red = cc = cc V = 1V 500Ω+ = 1.4kΩ (c) The requed V red = 6V, Since is positively proportional to the distance, assuming the distance is d, 6V = 1V 500Ω+ 6. Digital-Analog = 500Conversion Ω (a) For ideal op-amp, v 1 = v, therefore, by using KCL, vi v = o 1 f v o f = 500Ω d = 1.4kΩ 1cm d = 0.714cm

4 (b) Similar as before, by applying KCL at node a, v v v1 v v v v3 v i = i1+ i + i3 = + + Note that v a =0, the above equation becomes => a o a a a f 1 3 vo = v + v + v f f f (c) In fact, it s simply a binary representation (v 3 v v 1 ) of a decimal number ( v o ), which will be covered more in detail later. Therefore, the coefficients of v i must be as follows: f f f = 1; = ; = f f 1 = f ; = ; 3 = 4 This can be generalized as: f f 1 = f ; = ; L N = N 1 7. enewable Energy and Smart Grid (a) enewable energy is energy which comes from natural resources such as sunlight, wind, rain, tides, and geothermal heat, which are renewable (naturally replenished) Examples of renewable energy and its operation principles are as follows: Wind power: Aflows can be used to run wind turbines. The power output of a turbine significantly depends on the wind speed, so as wind speed increases, power output increases dramatically. Hydropower: Most hydroelectric power comes from the potential energy of dammed water driving a water turbine and generator. The power extracted from the water depends on the volume and on the difference in height between the source and the water's outflow. Solar power: Solar power process converse sunlight into electricity, either dectly using photovoltaics (PV), or indectly using concentrated solar power (CSP). Concentrated solar power systems use lenses or mrors and tracking systems to focus a large area of sunlight into a small beam. Photovoltaics convert light into electric current using the photoelectric effect. Biofuel: Energy of biofuel is derived from biological carbon fixation. It behaves as fossil fuel Geothermal power: Power plants take steam and water out of fractures in the

5 ground and use it to dectly drive a turbine that spins a generator. (b) Smart grid is a type of electrical grid which attempts to predict and intelligently respond to the behavior and actions of all electric power users connected to it, in order to efficiently deliver reliable, economic, and sustainable electricity services. Benefits of smart grid are as follows: Smart grid can create benefits through improvements in grid reliability by reducing the frequency and duration of power outages and the number of power quality disturbances, including reducing the probability of regional blackouts. Use of smart grid technologies can help mitigate or reduce the price of electricity through the interaction of the demand side of the market (consumers) with the supply side (suppliers). Smart grids can also create a platform on which retailers can create and offer new products and services that give consumers greater choice and flexibility in energy consumption and to create value for end users. Smart grid will promote envonmental quality by allowing customers to promote a more even deployment of renewable energy sources, and allow access to more envonmentally-friendly central station generation. Limitations of smart grid are as follows: Smart Grid has cyber security concerns. Power plant, power control system and power infrastructure can be attacked and shut down by hackers. Smart Grid will not work if consumers may not be willing to modify the energy usage behavior. It happens when pricing measures of the smart grid is complicated and volatile. Smart Grid cannot work unless all existing equipments are replaced by all meters, and communication network has been constructed. Large capital is requed. (c) Features of smart grid are as follows: Demand response support allows generators and loads to interact and be adjusted in an automated fashion in real time, coordinating demand to flatten spikes It has a greater resilience to loading Distributed generation allows individual consumers to generate power onsite, using whatever generation method they find appropriate. This allows individual loads to tailor the generation dectly to the load, making them independent from grid power failures. Price of electricity can be measured, calculated and adjusted in a real-time manner. This encourages people to use the electric power during night time or weekends.