In the combinations of resistors shown below. calculate:
the resistance across AB when the switch S is open.
Topic: Series-parallel resistor combinations
Answer
With the switch S OPEN, no current flows through the branch containing S, so each side of the network is just a 12 Ω and a 6 Ω in series.
Each branch: R₁ = 12 + 6 = 18 Ω
The two 18 Ω branches are in parallel between A and B: R = (18 × 18) ÷ (18 + 18) = 324 ÷ 36 = 9 Ω
Resistance across AB with S open = 9 Ω
An open switch is a break in the circuit: nothing flows through that path, so leave it out of the calculation entirely.
Two equal resistances in parallel give half of one of them, so 18 Ω and 18 Ω give 9 Ω without any working.
Do this part and part (b) together, because the comparison is the point of the question — closing the switch changes how the resistors are grouped.