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Question
Which of the following combinations have the same equivalent resistance between X and Y?
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Solution
Explanation:
1. In above first figure, the resistors are connected in parallel
Between X and Y.
Let Rp be their equivalent resistance.
Then,
`1/R_p=1/2+1/2`
`1/R_p=2/2`
Or, Rp = 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 RP, then
`1/"R"_"p" = 1/1 + 1/1 + 1/2`
`1/"R"_"p" = (2 + 2 + 1)/2`
`"R"_"p" = 2/5 Omega`
∴ RP = 0.4 Ω
Hence, RP = 0.4 Ω
3. In the circuit two resistors of 1 Ω each are connected in parallel. In parallel, the equivalent resistance is RP, then
`1/"R"_"p" = 1/1 + 1/1`
`1/"R"_"p" = (1 + 1)/1`
`1/"R"_"p" = 2/1`
`"R"_"p" = 1/2`
∴ RP = 0.5 Ω
Hence, RP = 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 RP, then
`1/R_p=1/2+1/2`
`1/R_p=2/2`
Or, Rp = 1 Ω
Hence, RP = 1 Ω
Therefore, on observing the values we can say that first and fourth have same equivalent resistances i.e., 1 Ω.
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