Question

show how would you connect 4 resistors each of resistance 1 ohm so that the combination has a resistance of 1- one ohm and second 2.5 ohm

Answer 1

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Answer 2

Answer:

Let the four resistors be R1,R2,R3 and R4.

(a) To get an effective resistance of 1 ohm, we need to connect the first two resistors( R1 and R2) in parallel and also the last two ( R3 and R4) in parallel and then the two parallel combinations in series.

Effective R of the first parallel combination:

1/R = 1/R1 + 1/R2 = 2 ohm

So R= 1/2 ohm

Effective resistance of the second parallel combination:

1/R' = 1/R3+ 1/R4 = 2 ohm

So R' =1/2 ohm

Now, connecting both in series: R+ R' = 1/2+1/2 = 1 ohm.

(b) Again, for getting an effective resistance of 2.5 ohm, we first connect the first two resistors ( R1 and R2) in parallel and then this combination is connected in series with the other two resistors( R3 and R4).

Effective resistance of the parallel combination:

1/R = 1/R1 + 1/R2 = 2 ohm

So R= 1/2 ohm = 0.5 ohm

Now for the series connection we have:

Effective resistance= R + R3 + R4 = 0.5+ 1+1 = 2.5 ohm.