Two resistances of 5.0 Ω and 7.0 Ω are connected in series and the com

Two resistances of 5.0 Ω and 7.0 Ω are connected in series and the combi- nation is connected in parallel with a resistance of 36.0 Ω. The equivalent resistance of the combination of three resistors is

24.0 Ω
12.0 Ω
9.0 Ω
6.0 Ω
This question was previously asked in
UPSC NDA-2 – 2024
The correct answer is C) 9.0 Ω.
First, calculate the equivalent resistance of the two resistors connected in series. For resistors in series, the equivalent resistance (R_series) is the sum of individual resistances:
R_series = R₁ + R₂ = 5.0 Ω + 7.0 Ω = 12.0 Ω.
Next, this series combination (with R_series = 12.0 Ω) is connected in parallel with a third resistance (R₃ = 36.0 Ω). For resistors in parallel, the reciprocal of the equivalent resistance (R_eq) is the sum of the reciprocals of the individual resistances:
1/R_eq = 1/R_series + 1/R₃
1/R_eq = 1/12.0 Ω + 1/36.0 Ω
To add the fractions, find a common denominator, which is 36.
1/R_eq = (3/36) + (1/36) = 4/36
1/R_eq = 1/9
R_eq = 9.0 Ω.
Understanding how to combine resistances in series and parallel is fundamental in circuit analysis. Resistances in series add directly, increasing the total resistance. Resistances in parallel combine in a way that the reciprocal of the total resistance is the sum of the reciprocals, resulting in a lower total resistance than the smallest individual resistance.
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