Circuits question

Feb 2020
2
0
London
Hello, I got this question that I can't seem to figure out, the questions is as follows: 4 lamps A,B,C and D will be connected in a circuit, put them in a way that D will light up the strongest, C will light up as the next strongest, A and B must have the same strength. I tried to do few figures and ended up with 3 possible figures that I think might be right but not sure which one of them. I need D to be stronger than C, C stronger than A, B, while A,B both have the same strength. Any help for which one is right and why the other ones are wrong would be greatly appreciated.
 

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Apr 2015
1,233
359
Somerset, England
This is a good question

Do you understand direct, series and parallel connections?

I assume that all four bulbs have the same resistance?
Call this R.

The light the bulb produces increase with bulb current.

So if A and B are connected in parallel they will have the same voltage across them.
Since their resistance is R for each they will also therefore have the same current in them.
So they will be equally bright.

If this combined current for A and B in parallel is fed from bulb C in series then each of A and B will see the half the current in C so A and B will be less bright than C.

The total resistance of the combination C + A//B is therefore R + R/2, which is greater than R.

So if This combination is connected directly across the battery its current will be less than the current in D if that bulb is also connected directly across the battery.

So D will be brighter than any of C, A or B
 
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Feb 2020
2
0
London
All 4 lamps are alike, so they must have the same R as you mentioned,

my thought was that the first figure and the last one will give you the same results, D be the brightest, therefore I connected it directly in series, since the current in a series circuit is always the same,

therefore the current of D = Current of C+ A*2, which would results D>C, but the tricky part is to make A,B equal while C being brighter than A or B

On the second figure where A and B are in series, since all lamps are alike, AB would have higher R than C, which makes C brighter since C has a lower R, and therefore I am leaning towards figure 2 as a solutions.
 
Apr 2015
1,233
359
Somerset, England
In your fig 1

How do you think A, B and C are connected?

Your fig 3 is the connection I described

Your fig 2

This will also work, can you see why?

What is the equivalent resistance of the bulbs A, B and C in relation to the overall circuit?
 
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Apr 2015
1,233
359
Somerset, England
Here are a couple of sketches

In (1) A and B are in parallel and in (2 )they are in series.
 

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