Question

calculate the effective resistance between a and b​

Answer 1

Answer:

The effective resistance between A and B = 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 + ...

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Solution :

4 Ω and 6 Ω are connected in series combination.

The equivalent resistance is equal to the sum of the individual resistances of resistors

= 4 Ω + 6 Ω = 10 Ω

3 Ω and 3 Ω are connected in series combination.

The equivalent resistance is equal to the sum of the individual resistances of resistors

= 3 Ω + 3 Ω = 6 Ω

Now, 10 Ω , 15 Ω and 6 Ω are in parallel combination.

The reciprocal of the equivalent resistance is equal to the sum of the reciprocals of individual resistances.

Let R be the effective resistance between A and B.

1/R = 1/10 + 1/15 + 1/6

 $\sf \dfrac{1}{R}=\dfrac{1 \times 3}{10 \times 3}+\dfrac{1 \times 2}{15 \times 2} +\dfrac{1 \times 5}{6 \times 5} \\\\ \sf \dfrac{1}{R}=\dfrac{3}{30}+\dfrac{2}{30}+\dfrac{5}{30} \\\\ \sf \dfrac{1}{R}=\dfrac{3+2+5}{30} \\\\ \sf \dfrac{1}{R}=\dfrac{10}{30} \\\\ \longrightarrow \boxed{\tt R=3 \Omega}$

Therefore, the effective resistance between A and B = 3 Ω

         

Answer 2

Answer:

The answer is 3

Explanation:

as 6+4 is 10

3+3 is 6

then 1/6+1/10+1/15

3....is the answer then...