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As homework, I have to design a circuit (in the form of a circuit diagram) to power three given lamps optimally (so that they receive the exact current and voltage they need) with any number of 1.5 V batteries and any number of arbitrary resistors.

The three lamps are: 0.15A/8V, 0.20A/5V and 0.12A/4V. The designed circuit needs to be optimal in the sense that the power consumption to power the three lamps needs to be as small as possible.

Currently, my best (and only) bet is this one:

+---[3]---[42Ω]---+   [3]=0.12A/4V
|                 |
+---[2]---[20Ω]---+   [2]=0.20A/5V
|                 |
+---[1]---[6.7Ω]--+   [1]=0.15A/8V
|                 |
+-- 6 batteries --+

Can't post images yet, therefore this crappy sh** stuff. batteries 9V indicates the position of the 6 1.5V batteries amounting to 9V. (As a side note, the resistor values are rounded to 2 significant digits, and could mathematically be \$41\frac{2}{3}\Omega\$, \$20\Omega\$ and \$6\frac{2}{3}\Omega\$. Also, the comma is supposed to be a decimal point.)

Is there a better solution than this one (with a consumption of 4.23W), and if so, how would I arrive at that solution?

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  • \$\begingroup\$ Just to widen mental filters. What would happen if you placed the 8V and 4V bulbs in SERIES, powered them from 8 x 1.5V and placed a 133 Ohm resistor in PARALLEL with the 4V bulb. That may well not be part of an optimum solution (or may) , but may suggest other possibilities. \$\endgroup\$
    – Russell McMahon
    Apr 10, 2013 at 3:44
  • \$\begingroup\$ Since you do not have sufficient reputation yet to post images as part of a question, please upload your schematic to any public image sharing site, then provide the link as a comment to your own question. Someone with editing rights will typically incorporate the image into the question for you. Commendable effort with the ASCII art, by the way :-) \$\endgroup\$ Apr 10, 2013 at 3:57
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    \$\begingroup\$ +1, Upvoting to counter the anonymous fly-by downvote: This question indicates a fair amount of effort towards solving the problem, before posting as a question, hence deserves some support. \$\endgroup\$ Apr 10, 2013 at 3:58

1 Answer 1

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Yes, there are several solutions which have less power consumption than the sketched common-parallel circuit of 4.23 W. Given that this is an exercise, you need to explore the situation to develop your understanding. Try working on these things:

  1. What's the minimum power consumption of any circuitry for the three lamps using batteries of any voltage whatsoever?
  2. What set of circuit connections would give you that consumption?
  3. If you could use any number of 1V batteries (instead of 1.5V), could you build the circuitry of step 2? What would it look like?
  4. Keeping everything the same except the number of batteries, what would the minimal power consumption of the circuitry be if you had to use 1.5V batteries instead of 1V batteries?
  5. Is that consumption better than 4.23W?
  6. Now explore other arrangements of lamps after thinking about these things:

    • any power consumed by a resistor you add is wasted

    • a lamp itself has a resistance, and can serve as a resistor

    • if a lamp serves as a resistor, it saves the power the resistor would have used

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    \$\begingroup\$ +1, good work teaching 'em to fish instead of handing them the fish. \$\endgroup\$ Apr 10, 2013 at 3:59
  • \$\begingroup\$ Thanks, I'll think about tese things. And indeed this is an exercise so it's good that you let me do something, I suppose... :) \$\endgroup\$
    – tomsmeding
    Apr 10, 2013 at 5:24

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