An electrician has two resistive coils. He can obtain the resistance of 3 ohm, 4 ohm, 12 ohm and 16 ohm by keeping them alone and by connecting them in series and parallel. The resistance of these two coils are how much in ohms?

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Solution

When resistances connected in series,the total resistance will be greater than the maximum individual resistance connected.
ie,if 2 ohm and 4 ohm are connected.Total resistance 6 ohm will be greater than 4.
When connected in parellel, the total resistance will be lesser than the minimum individual resistance connected.
ie, 2 ohm 4 ohm connected.total resistance 4/3 ohm will be lesser than 2 ohm

Here maximum resistance given is 16 ohm.So it is the total resistance when connected in series.
3 ohm is the smallest one.So it is obtained when connected in parellel.
So 4 ohm and 12 ohm are the resistances of the coils.
12+4=16 ohm -----series resistance
1/R=(1/12)+(1/4)=1/3⇒ 3 ohm will be the parellel resistance.

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