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Short method to answer this question How will you join three resistors  of resistance 4 ohm, 6 ohm and 12 ohm to get an equivalent resistance of 8 ohm. 
Asked by rishijuneja2018 | 22 Apr, 2018, 05:46: PM
answered-by-expert Expert Answer
when resistances are connected in parallel, we get equivalent resistance which is less than the individual resistances of the parallel combination.
Since we need 8Ω as final value, all three resistances connected in parallel is ruled out, because the equivalent resistance in this case will be less than 4Ω.
 
The highest value of the given resistances is 12Ω. We should bring down this higher resistance 12Ω. Hence either 12Ω is connected parallel with 6Ω or 4Ω and this parallel combination should connected in series with the left out resistance. 
 
(a) let us consider 12Ω and 4Ω connected paralel and this parallel combination is connected to 6Ω.
 
equivalent resistace of 12Ω and 4Ω conneted parallel = (12 × 4)/(12 + 4) = 3Ω
when this 3Ω connected in series with 6Ω gives net resistance 9Ω
 
(b) let us consider 12Ω and 4Ω connected paralel and this parallel combination is connected to 6Ω.
 
equivalent resistace of 12Ω and 6Ω conneted parallel = (12 × 6 )/(12+6) = 4Ω
when this 4Ω connected in series with 4Ω gives net resistance 8Ω
 
Answer:- connect 12Ω and 6Ω parallel, then connect this parallel combination to 4Ω in series
Answered by Thiyagarajan K | 22 Apr, 2018, 09:51: PM

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