Question

Two resistors3Ωand 6Ω are connected first in series and then in parallel. The

ratio of the effective resistors will be 1 mark

a) 2:9

b) 1:3

c) 9:2

d) 1:2​

Answer 1

Answer:

2/9

1/3

9/2

1/2

is the answer

Answer 2

Solution :-

Given ,

• Two resistors ( R₁ & R₂ ) are connected in series & parallel
• Resistor 1 ( R₁ ) = 3 Ω
• Resistor 2 ( R₂ ) = 6 Ω

We need to find ,

• Ratio of the resistors when connected in series & parallel

As we know that,

• Resistors connected in series → Rₙ = R₁ + R₂
• Resistors connected in parallel → 1/Rₙ = 1/R₁ + 1/R₂

• Resistors connected in series :-

→ Rₙ = 3 + 6

→ Rₙ = 9 Ω

∴ Resistance connected in series = 9Ω

• Resistance connected in parallel :-

→ 1/Rₙ = 1/3 + 1/6

→ 1/Rₙ = ( 6 + 3 )/3×6

→ 1/Rₙ = 9/18

→ 1/Rₙ = 1/2

By cross - multiplying

→ Rₙ = 2 Ω

Resistance connected in parallel = 2Ω

________________________

Now , Resistance connected in series : Resistance connected in parallel

⇒ Rₛₑᵣᵢₑₛ : Rₚₐᵣₐₗₗₑₗ = 9 : 2

∴ Hence , Rₛₑᵣᵢₑₛ : Rₚₐᵣₐₗₗₑₗ = 9 : 2 . So , option (C) is your answer .