Question

Calculate the equivalent resistance between points A and B ​

Answer 1

answer in attachment

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Answer 2

Answer:

40/3 Ω

Explanation:

To know :  

• When resistors of resistances R₁ , R₂ , R₃ .... are connected in series, the equivalent resistance is given by

R = R₁ + R₂ + R₃ + ...  

• When resistors of resistances R₁ , R₂ , R₃ .... are connected in parallel, the equivalent resistance is given by

1/R = 1/R₁ + 1/R₂ + 1/R₃ + ...

Solution :

[Refer to the attachment]

R₄ and R₅ are connected in series. So, the equivalent resistance of these two resistors is

R₄₅ = R₄ + R₅

R₄₅ = 5 Ω + 5 Ω

R₄₅ = 10 Ω

Replace R₄ and R₅ with a single resistor of resistance R₄₅ ( = 10 Ω)

Now, R₄₅ and R₂ are connected in parallel combination.

 The equivalent resistance for this combination is :

 $\rm \dfrac{1}{R_{245}} = \dfrac{1}{R_2}+\dfrac{1}{R_{45}} \\\\ \rm \dfrac{1}{R_{245}} = \dfrac{1}{5}+\dfrac{1}{10} \\\\ \rm \dfrac{1}{R_{245}} = \dfrac{3}{10} \\\\ \rm R_{245} = \dfrac{10}{3}$

⇒ R₂₄₅ = 10/3 Ω

R₂₄₅ , R₁ & R₃ are connected in series.

So, the equivalent resistance = R₂₄₅ + R₁ + R₃

 R₁₂₃₄₅ = 10/3 + 5 + 5

 R₁₂₃₄₅ = 10/3 + 10

 R₁₂₃₄₅ = 40/3 Ω

∴ The equivalent resistance between points A and B is 40/3 Ω.