Question

find equivalent resistance​

Answer 1

Answer:

The required equivalent resistance is 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]

R₁ = R₂ = R₃ = 4

R₄ = 12

R₅ = 3

R₆ = R₇ = 0.5

R₁, R₂, R₃ are connected in series. Let R₁₂₃ be it's equivalent resistance.

R₁₂₃ = R₁ + R₂ + R₃

R₁₂₃ = 4 + 4 + 4

R₁₂₃ = 12

R₁₂₃, R₄, R₅ are connected in parallel combination. Let R₁₂₃₄₅ be it's equivalent resistance.

1/R₁₂₃₄₅ = 1/R₁₂₃ + 1/R₄ + 1/R₅

1/R₁₂₃₄₅ = 1/12 + 1/12 + 1/3

1/R₁₂₃₄₅ = (1+1)/12 + 1/3

1/R₁₂₃₄₅ = 2/12 + 1/3

1/R₁₂₃₄₅ = 1/6 + 1/3

1/R₁₂₃₄₅ = (1+2)/6

1/R₁₂₃₄₅ = 3/6

1/R₁₂₃₄₅ = 1/2

R₁₂₃₄₅ = 2

R₁₂₃₄₅, R₆, R₇ are connected in series. Let R₁₂₃₄₅₆₇ be the equivalent resistance.

R₁₂₃₄₅₆₇ = R₁₂₃₄₅ + R₆ + R₇

R₁₂₃₄₅₆₇ = 2 + 0.5 + 0.5

R₁₂₃₄₅₆₇ = 2 + 1

R₁₂₃₄₅₆₇ = 3

Therefore, the equivalent resistance is 3 Ω