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How can three resistors of resistances 2 Ohms , 3 Ohms and 6 Ohms be connected to give total resistance of (i) 4Ohms (ii) 1Ohm

For total Resistance to be 4

we will connect 2 ohm resistance in series with parallel combination of 3 and 6 ohm resistance.

When 3 and 6 ohm are in parallel combination then 1/R=1/3+1/6= > R=2

Now this R connected in series with 2 ohm resistance will give equivalent resistance = 2+ 2 = 4 ohm.

 

For total Resistance to be 1 ohm

All the given resistance should be connected in parallel combination

1/R'=1/2+1/3+1/6 => R'=1 ohm

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1) 1st connect 3ohm resistant and 6ohm resistant in parallel, then you will get a equivalent resistant of,

  1/3 + 1/6 = 1/2 = 2ohm.

  Now, connect this eqivalent resistant of 2ohm. with the 2ohm resistant you have in series.

  Then you get a total resistant of = 2+2 = 4ohm resistance.

2) connect all the 3 resitors in parallel.

  Then, the equivalent resistance will be,

  1/2 + 1/3 + 1/6 = 6/6 = 1 ohm

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