Question

How will you connect three resistances each of 6 ohms so that
resultant resistance would be 9 ohms and 4 ohms ?​

Answer 1

Answer:

To get total resistance 9 you have to connect 2 resistance in parallel and one in series. To get resistance 4 ,

Answer 2

Given :

We are given three resistances each of 6Ω.

To Find :

How should we connect these resistors to get equivalent resistance of 9Ω and 4Ω.

Solution :

❖ In order to get equivalent resistance of 9Ω, we need to connect two parallel resistors in series with third resistor$.$

Equivalent of parallel connection will be

» R₁₂ = R₁R₂ / (R₁ + R₂)

» R₁₂ = 6 × 6 / (6 + 6)

» R₁₂ = 36/12

» R₁₂ = 3Ω

Finally R₁₂ and R₃ come in series so net equivalent resistance will be

➙ R = R₁₂ + R₃

➙ R = 3 + 6

➙ R = 9Ω

❖ In order to get equivalent resistance of 4Ω, we need to connect two resistors in series with third resistor in parallel.

In upper branch two resistors are connected in series so their equivalent will be 12Ω.

Finally, 12Ω and 6Ω come in parallel!

➙ 1/R = 1/R₁₂ + 1/R₃

➙ 1/R = 1/12 + 1/6

➙ 1/R = 1/12 + 2/12

➙ 1/R = 12/3

➙ R = 4Ω