Practice portal › Current Electricity › Combination of Resistors
Asked in GUJCET 2019 · Symmetric and complex networks
Given (figure): six equal resistors of 2 Ω. Between X and Y there is an upper branch (two in series), a lower branch (two in series), a cross link joining the midpoints of these branches, and one resistor joining X to Y directly.
Idea: the upper and lower branches are identical, so their midpoints are at the same potential; the cross link carries no current and can be removed (a balanced bridge).
Each branch: 2 + 2 = 4 Ω; the two branches in parallel give (4×4)/(4 + 4) = 2 Ω.
This 2 Ω is in parallel with the direct 2 Ω: R_XY = (2×2)/(2 + 2) = 1 Ω.
So the equivalent resistance between X and Y is 1 Ω (half of one resistor).
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