Question

You are given three equal resistors. The number of resistance which can be obtained by joining them in series and in parallel grouping is

Answer 1

4 resistances can be formed by series and parallel combination of all 3 resistances.

Consider 3 resistances each of value R.

1. When all three are connnected in a seriescombination the equivalent resistance is 3R.

2. When any two of them are connected in paralleland one in series with them the equivalent resistance will be

(R×R/(R+R))+R=R/2+R=3/2R

3. When any two of them are connected in series and one is connected in parallel then the effective resistance will be

(2R×R/(2R+R))=2/3R

4. When all three resistances are connected in parallel then the effective resistance will be

From point no.2 we can take the resistance of two resistances in parallel which is R/2

Hence the equivalent of three parallel will be R/2×R/(R/2+R)=R/3

Two more resistances can be obtained by putting any two in series(2R) and any two in parallel(R/2).

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Answer 2

In series the number of resistance obtained are 4
In parallel the number of resistance obtained is 3


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