Foundations of Electrical Engineering Assignment - DC CIRCUIT DESIGN CHALLENGE
Cyril the cyclist proudly shows you his new bicycle, complete with LED front and rear lights and a battery and generator (hub dynamo) to power them. You suggest Cyril could charge his mobile phone as he rides. Cyril thinks this is a revolutionary idea and asks you to make it work.
First you examine the existing lighting system. The front LED is attached to the handlebars; the rear LED is mounted under the seat along with the battery. Both the LEDs and the battery are modelled as voltage sources with an internal series resistance. The permanent magnet generator is located in the front wheel hub, and acts as a voltage source where voltage is proportional to speed. A diode is connected in series with the generator so that the battery is not discharged when the bicycle is stopped or moving slowly. Resistors Rx and Ry set the LED currents. The positive terminals of the LEDs, battery and generator are connected together in parallel by a thin wire; the negative terminals are all connected using the bicycle's conductive aluminium frame.
The USB charger circuit you find limits the current to the phone to 0.5 A, so long as the voltage across the circuit including the phone is 6.5 V or greater. The USB charger circuit is connected on the handlebars next to the front LED light, and is modelled as a current source.
In the most bizarre coincidence, you note that the parameters of these sources and loads can be derived from your student number as follows:
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Circuit Element
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Symbol
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Formulae
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Example value for student # 6324715
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Generator internal resistance
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a Ω
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(Digit 1 * 0.2) + 2
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(6 * 0.2) + 2 = 3.2 Ω
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Generator constant (V/rpm)
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b V/rpm
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(Digit 2 * 0.001)+ 0.04
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(3*0.001)+0.04=0.043V/rpm
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Wire resistance
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c Ω
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(Digit 3 * 0.02) + 0.3
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(2 * 0.02) + 0.3 = 0.34 Ω
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Battery internal series resistance
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d Ω
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(Digit 4 * 0.01) + 0.2
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(4 * 0.01) + 0.2 = 0.24 Ω
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Battery internal voltage
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e V
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(Digit 5 * 0.1) + 7.2
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(7 * 0.1) + 7.2 = 7.9 V
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LED internal series resistance
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f Ω
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(Digit 6 * 0.3) + 6
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(1 * 0.3) + 6 = 6.3 Ω
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LED light internal voltage drop
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g V
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(Digit 7 * 0.04) + 5
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(5 * 0.04) + 5 = 5.2 V
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Note: The values provided in the fourth column show the calculation of the parameters for student number 6324715. Do not use these values, they are an example only. Derive values from your own student number.
Explanations of steps used are essential, and will be carefully accounted for in assessment. Best marks are awarded to numerically correct solutions, but partial credit will be given to partially complete solutions or incorrect solutions where errors have carried through the calculations. State any and all assumptions that you make.
(a) Ignoring all of the circuit except for the battery and rear LED, calculate the value of the resistor Rx between the battery and the rear LED so that the LED current is 50 mA. (Note that when the complete circuit is operating, the rear LED current will change.) Use this value of resistor Rx for both resistors Rx and Ry in the remainder of your calculations.
(b) Calculate the output voltage of Cyril's generator when he is riding at 30 km/h.
(c) Draw the circuit diagram of the system described above, labelling components with values as calculated from your student number. Where possible, simplify the diagram by combining series and parallel resistances and sources.
(d) Using a circuit analysis technique of your choosing, calculate the current flowing in each LED, the battery, and the generator when the bicycle is travelling at 30 km/h. The phone charger is disconnected (switch Sw1 is open). Calculate the power balance of the system. Remember to show all working. Using these power calculations, comment on the effectiveness of power transfer from the generator to (or from) the battery, and to each LED light (calculate percentages).
(e) Now you test the phone charger (switch Sw1 is closed). What is the new operating current for each LED, the battery and the generator when the bicycle is travelling at 30 km/h? Calculate the voltage across the phone charger to check it is more than 6.5 V. Show all working.
(f) Use circuit simulation software to verify your calculations in (d) and (e). Show sufficient screen shots of the software to verify your calculations are correct.
(g) At the end of a 40 minute, 30 km/h ride, what amount of charge (in mAh) has been added to the phone? And added to or removed from the bicycle battery?
(h) What is the minimum speed that Cyril needs to cycle to ensure that his battery does not slowly discharge and go flat? Assume that the phone charger is disconnected. Show all working.
Attachment:- Assignment File.rar