Question

Four resistances of 2.0Ω each are joined end to end to form a square ABCD. Calculate the equivalent resistance of the combination between points A and B.​

Answer 1

Given :

Four resistors of 2Ω each are joined end to end to form a square ABCD.

To Find :

Equivalent resistance between points A and B$.$

Solution :

Equivalent resistance of series :-

• R = R₁ + R₂ + ... + Rₙ

Equivalent resistance of parallel :-

• 1/R = 1/R₁ + 1/R₂ + ... + 1/Rₙ

Resistor b/w AB = R₁

Resistor b/w BC = R₂

Resistor b/w CD = R₃

Resistor b/w AD = R₄

❇ From the attached image, it is clear that R₂, R₃ and R₄ are connected in series.

➝ R₂₃₄ = R₂ + R₃ + R₄

➝ R₂₃₄ = 2 + 2 + 2

➝ R₂₃₄ = 8Ω

Finally R₂₃₄ and R₁ come in parallel,

➠ 1/R = 1/R₁ + 1/R₂₃₄

➠ 1/R = 1/2 + 1/8

➠ 1/R = (4 + 1) / 8

➠ R = 8/5

➠ R = 1.6Ω