Question

Show how would you connect three resistors of 9 ohm each so that the equivalent resistance of combination is a) 13.5 ohm b)6 ohm

Answer 1

I hope it will help you

Answer 2

We can connect the three resistors in the following way:

(a) First two resistance connected in parallel and the resulted is connected with another resistor in series. Equivalent resistance of combination is 13.5 ohm

(b) First two resistance connected in series and the resulted is connected with another resistor in parallel. Equivalent resistance of combination is 6 ohm.

We know, for 2 resistances, R₁ and R₂, the equivalent resistance:

(1) When connected in series is

R =  R₁ + R₂

(2) When connected in parallel is

R = (R₁ × R₂)/(R₁ + R₂)

Here, in the question, R₁ = R₂ = R₃ = 9Ω

(a) When R₁ and R₂ are first connected in parallel,

Equivalent resistance R' = (9 × 9)/(9 + 9)Ω = 81/18Ω = 4.5Ω

Again when the third resistance R₃ is connected to R' in series, we get equivalent resistance as R = (4.5 + 9)Ω = 13.5Ω

(b) When R₁ and R₂ are first connected in series,

Equivalent resistance R' = (9 + 9)Ω = 18Ω

Again when the third resistance R₃ is connected to R' in parallel, we get equivalent resistance as R = (18 × 9)/(18 + 9)Ω = cΩ = 6Ω