Question

Which of the following combinations have the same equivalent resistance between X and Y?

विकल्प

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Answer 1

 

Explanation:

1. In above first figure, the resistors are connected in parallel

Between X and Y.

Let R_p be their equivalent resistance. 

Then, 

`1/R_p=1/2+1/2`

`1/R_p=2/2` 

Or, R_p = 1 Ω    ...(i)

In the circuit there are three parts. In the first part two resistor of 1 Ω each are connected in series.

In series, the equivalent resistance is R'_S, then

R'_S = (1 + 1) Ω = 2 Ω

2. In the circuit, three resistors of 1 Ω, 1 Ω and 2 Ω are connected in parallel. In parallel, the equivalent resistance is R_P, then

`1/"R"_"p" = 1/1 + 1/1 + 1/2`

`1/"R"_"p" = (2 + 2 + 1)/2`

`"R"_"p" = 2/5 Omega`

∴ R_P = 0.4 Ω

Hence, R_P = 0.4 Ω

3. In the circuit two resistors of 1 Ω each are connected in parallel. In parallel, the equivalent resistance is R_P, then

`1/"R"_"p" = 1/1 + 1/1`

`1/"R"_"p" = (1 + 1)/1`

`1/"R"_"p" = 2/1`

`"R"_"p" = 1/2`

∴ R_P = 0.5 Ω

Hence, R_P = 0.5 Ω

4. In the circuit there are three parts. In the first part two resistor of 1 Ω each are connected in series. In series, the equivalent resistance is R'_S, then

R''_S = (1 + 1) Ω = 2 Ω

In the third part, R'_S and R''_S are in parallel, the equivalent resistance is R_P, then

`1/R_p=1/2+1/2`

`1/R_p=2/2` 

Or, R_p = 1 Ω 

Hence, R_P = 1 Ω

Therefore, on observing the values we can say that first and fourth have same equivalent resistances i.e., 1 Ω.