Question

Find the equivalent resistance? ​

Answer 1

Solution!!

The concept of resistance in parallel and series circuit has to be used here. We will start calculations from the right side of the circuit.

Formulae to be used:-

Rₛ = R₁ + R₂ + R₃ + R₄ + ... Rₙ

1/Rₚ = 1/R₁ + 1/R₂ + 1/R₃ + 1/R₄ + ... 1/Rₙ

Here, Rₛ is resistance in series circuit and Rₚ is resistance in parallel circuit.

Starting from the right side of the circuit, the resistance is in series circuit.

Rₛ = 2Ω + 2Ω + 2Ω

Rₛ = 6Ω

The arrangement is shown in fig 1 in the attachment.

Now, the arrangement is in parallel circuit.

1/Rₚ = 1/6 + 1/6

1/Rₚ = 2/6

1/Rₚ = 1/3

Rₚ = 3Ω

The arrangement is shown in fig 2 in the attachment.

Now, again the arrangement is in series circuit.

Rₛ = 6Ω + 3Ω + 6Ω

Rₛ = 15Ω

The arrangement is shown in fig 3 in the attachment.

Now, again the arrangement is in parallel circuit.

1/Rₚ = 1/18 + 1/15

1/Rₚ = (6 + 5)/90

1/Rₚ = 11/90

Rₚ = (90/11)Ω or 8.18Ω

The arrangement is shown in fig 4 in the attachment.

Lastly, the arrangement is in series circuit.

Rₛ = 2Ω + (90/11)Ω + 2Ω

Rₛ = 4Ω + (90/11)Ω

Rₛ = (44 + 90)/11 Ω

Rₛ = (134/11)Ω or 12.18Ω

Hence, the equivalent resistance from A to B is (134/11)Ω or 12.18Ω.