  Question

An electrician has 2 resistor coil. He can obtain resistance 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 coils are how much in ohms?

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.  Physics

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