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Find the equivalent resistance between terminals a and b of the circuit as shown in figure (a) and (b). Each resistor has a value of 1Ω.

Concept: Equivalent Resistance Cube Circuits

Question

Find the equivalent resistance between terminals a and b of the circuit as shown in figure (a) and (b). Each resistor has a value of 1Ω.
A) 5/11 Ω, 5/12 Ω
B) 5/11 Ω, 7/12 Ω
C) 7/11 Ω, 5/12 Ω
D) 7/11 Ω, 7/12 Ω
Req=V/IR_{eq} = V/I

Try it yourself first

Hint: For circuit (a), identify the points that are at the same potential due to symmetry when current enters at 'a' and leaves at 'b'.

Step-by-step solution

  1. 1

    Circuit (a) Symmetry

    Current at 'a' • Splits equally
  2. 2

    Circuit (a) Reduction

    Symmetry • Same potential points • Redraw circuit
    Req=711RR_{eq} = \frac{7}{11}R
  3. 3

    Circuit (b) Symmetry

    Body diagonal • Current splits
  4. 4

    Circuit (b) Reduction

    Symmetry • Equipotential points • Series/Parallel
    Req=712RR_{eq} = \frac{7}{12}R
  5. 5

    Final Calculation

    R = 1 Ohm • Substitute values
    Req,a=711Ω,Req,b=712ΩR_{eq,a} = \frac{7}{11} \Omega, R_{eq,b} = \frac{7}{12} \Omega

Final answer

D) 7/11 Ω, 7/12 Ω

Remember: Symmetry simplifies complex resistor networks into simpler series/parallel combinations.

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When calculating the equivalent resistance of a symmetrical circuit, which of the following is a valid simplification technique?

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