Question

3 identical resistance is 10 ohm are joined form a triangle the equivalent resistance between2 2 comers of the triangle is ​

Answer 1

Given :

Three identical resistors of 10 Ω are joined as they form a triangle.

To Find :

Equivalent resistance between any two corners of the triangle.

Solution :

Equivalent resistance of series :

• R = R₁ + R₂ + ... + Rₙ

Equivalent resistance of parallel :

• 1/R = 1/R₁ + 1/R₂ + ... + 1/Rₙ

Let resistance between A & B be R₁, between B & C be R₂ and between A & C be R₃.

Now let's find equivalent resistance between A and B.

From the attached image, it is clear that R₂ and R₃ are connected in series$.$

Hence equivalent resistance of that series will be

➠ R₂₃ = R₂ + R₃

➠ R₂₃ = 10 + 10

➠ R₂₃ = 20 Ω

Finally R₂₃ and R₁ come in parallel.

So net equivalent resistance will be

➠ 1/R = 1/R₁ + 1/R₂₃

➠ 1/R = 1/10 + 1/20

➠ 1/R = (2 + 1) / 20

➠ R = 20/3

➠ R = 6.66 Ω