Question

Using a circuit analysis technique of your choosing, calculate the power balance of the system at midday. Show all working. Comment on the effectiveness (calculate percentages) of power transfer from the solar panel to the LED lights, and how much is dissipated in the wiring. If LED brightness is proportional to current, express the relative brightness of the LED lights if LED 3 is used as a reference (100%),

a=560

b=0.92

c=28

d=2.8

e=2.4

f=6.6

g=31.5

Sarah the sommelier wants to use a skylight to brighten the dim wine cellar of her new restaurant. Sarah has a brilliant idea she will design an "electric skylight". In order to do that, she will install a solar panel on the roof, which can directly power three LED lights in the cellar with only wires connecting them. A long two core cable (positive and negative connection) connects the solar panel to the first LED light (distance c metres), and then two short lengths link two more LED lights (separated by distances d and e metres, all as marked on the diagram). The 1 sq mm cable used has a resistance of 0.03 2 per metre per core. The solar panel is modelled as a Norton equivalent source, while the LED lights are modelled as Thévenin voltage sources. Note: solar panels and LED lights are actually more complex than this, but assume that they behave this way unless you are given specific details about the components used by Sarah] c m e m c m Im e m Solar panel LED light 1 LED light 2 LED light 3 Figure 1. Sarah's design. As an enthusiastic future electrical engineer, Sarah asks for your help to analyse her proposed system when you visit. The values of the circuit elements and wire lengths have been emailed to you.

Answer 1

Bring down the top line to bottom to simplify the circuit 28 Ω 2.8Ω V, 2.4 Ω LED3 LED2 SP 6.6 Ω 6.6 Ω 6.6 Ω 0.92 A 560 Ω 31.5 31.5 31.5 2.4 Ω 2.8 Ω,3 28 Ω Convert the current source in solar panel to voltage source. V IR (0.92) (560) 515.2 V Draw the modified circuit 28(2 2.4 Ω V, 2.8 Ω LED3 LED2 SP 6.6 Ω 6.6 Ω 6.6 Ω 560 Ω 31.5 31.5 31.5 515.2 V V, 2.8Ω 2.4 Ω 28 Ω

Write the KVL equation for loop i -515.2 5601 +281 +6.6( -1)+31.5+2810 622.6/, -6.6I, - 483.7 Write the KVL equation for loop i -31.5 +6.6(12-I)+2.812 +2.812+ 6.6(12-1)+31.5 0 -6.61 +18.8I, -6.6/, -0 Write the KVL equation for loop i -3 1.5 +6.6(13-12-24 6.613 +3 1.5+2.41,-0 -6.61, +187, =0 Solve the equations (1), (2) and (3) I, -0.78 A I, 0.314 A I3 -0.115 A Calculate the power delivered by the solar panel. P (515.2)4 () (560) = (515.2)(0.78)-(0.78)" (560) P. = 61.152 W Calculate the power dissipated by the LED 1. Pu (31.5)(4)+(-1) (6.6) =(31.5)(0.78-0.314)-(078-0314)"(66) Pu-16.11 W

Calculate the power dissipated by the LED 2 (31.5)(0.314-0.115)+(0.314-0.115) (6.6) P 6.53 w Calculate the power dissipated by the LED 3. Eg-(31.5)(4)-(4). (6.6) (31.5) (0.115)+(0.115) (6.6) P,,-371W Calculate the total power dissipated in LED lights 16.11+6.53+3.71 P 26.35 W Calculate the percentage of transferred from the solar panel to the LED lights LED 10090 90 power :- 26.35 x1 0090 61.152 %power-43.089% Calculate the power dissipation in wiring Prinx -(1) 28+(1,) 28+(72) 2.8+(/2) 2.8+(I) 2.4+(1,) 2.4 2(0.78) (28)2(0.314) (2.8)+2(0.115) (2.4) - 34.07+ 0.552+0.0635 uiting 34.685 w