Consider the following combination of resistors : [Diagram of resistor

Consider the following combination of resistors :
[Diagram of resistors]
The equivalent resistance of the combination of resistors between P and Q is

2 Ω
3 Ω
3.5 Ω
2.5 Ω
This question was previously asked in
UPSC Geoscientist – 2023
Assuming the diagram represents two parallel branches connected between points P and Q, with one branch consisting of two 3 Ω resistors in series and the other branch being a single 6 Ω resistor:
Let R₁ and R₂ be the resistances in the first branch. Since they are in series, their equivalent resistance R_series1 = R₁ + R₂ = 3 Ω + 3 Ω = 6 Ω.
Let R₃ be the resistance in the second branch. R₃ = 6 Ω.
These two equivalent resistances (R_series1 and R₃) are connected in parallel between P and Q. The equivalent resistance of two resistors in parallel is given by R_eq = (R_a * R_b) / (R_a + R_b).
R_eq = (R_series1 * R₃) / (R_series1 + R₃) = (6 Ω * 6 Ω) / (6 Ω + 6 Ω) = 36 Ω² / 12 Ω = 3 Ω.
The equivalent resistance of the combination of resistors between P and Q is 3 Ω.
Resistors in series add directly (R_total = ΣR_i). Resistors in parallel combine as the reciprocal of the sum of reciprocals (1/R_total = Σ1/R_i).
This problem requires identifying series and parallel combinations within a circuit diagram. Analyzing the connections from one terminal to the other helps in breaking down the circuit into simpler parts. Series connections occur when components are connected end-to-end along a single path. Parallel connections occur when components are connected across the same two points.