Question

A wire of resistance 18Ω is cut into 3 equal parts .These 3 equal parts are
connected in parallel. Find the
i) Resistance of each part.
ii) Effective resistance of the combination.

Answer 1

Solution :-

Given ,

• Total resistance of wire = 18 Ω
• The wire has cut into 3 equal parts
• And then connected in parallel

We need to find ,

• i) Resistance of each part
• ii) Equivalent or effective resistance.

As we know that ,

• If the wire has cut into equal parts then the resistance of three parts is also equal .
• If three resistors are connected in parallel → 1/Rₙ = 1/R₁ + 1/R₂ + 1/R₃

• Resistance of each part :-

⇒ 18/3

⇒ 6Ω

Hence , resistance of each part = 6Ω

• Resistance when connected in parallel :-

⇒ 1/Rₙ = 1/6 + 1/6 + 1/6

⇒ 1/Rₙ = 3/6

⇒ 1/Rₙ = 1/2

⇒ Rₙ = 2 Ω

Hence , resistance when connected in parallel = 2 Ω

Answer 2

Answer :-

• Resistance of each part is 6Ω.
• Resistance connected in parallel is 2Ω.

Given :-

• A wire of resistance 18Ω is cut into 3 equal parts and these 3 equal parts are
• connected in parallel.

To Find :-

• Resistance of each part.
• Effective resistance of the combination.

Solution :-

If three resistors are connected in parallel,

Then

1/Rⁿ = 1/R1 + 1/R2 + 1/R3

Here

Resistance of each part :-

→ 18/3

→ 6Ω

Hence, resistance of each part is 6Ω.

Resistance connected in parallel :-

1/Rⁿ = 1/6 + 1/6 + 1/6

→ 1/Rⁿ = 3/6

→ 1/Rⁿ = 1/2

→ Rⁿ = 2Ω

Hence, resistance connected in parallel is 2Ω.