Short Note

Three resistors each of 2Ω are connected together so that their total resistance is 3Ω. Draw a diagram to show this arrangement and check it by calculation.

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#### Solution 1

A parallel combination of two resistors, in series with one resistor.

R_{1} = 2 ohm

R_{2 }= 2 ohm

R_{3} = 2 ohm

`1/"R" =1/"R"_1+1/"R"_2`

`I/"R"=1/2+1/2=1`

`"R" = "R"+ "R"_3 = 1 + 2 = 3 ohm`

#### Solution 2

The given diagram of the arrangement is shown in figure in which two resistors are in parallel and then this combination is in series with one resistor.

The equivalent resistance of parallel combination:

R' = `(2 xx 2)/(2 + 2) = 4/4 = 1 Omega`

Then total resistance of series combinations of R’ = 1Ω with 2Ω resistors is R = 1 + 2 = 3Ω.

Concept: System of Resistors - Resistances in Parallel

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