Question

★Question for Physics experts★

Find the equivalent resistance between A and B, when resistance of each resistor is R.
Good explaination needed. Also add simplified circuit if possible.

[Hint-Use folding symmetry rule]

JEE mains Question

Answer 1

Here in this question we are asked to find equivalent resistance between A and B.

Resistance of each resistor is R.

Considering folding symmetry across CE.

Hence C and E are at same potential. Similarly D and F are at same potential.

• Those two resistors between CE and DF won't be considered in the calculation.

$\bf Potential\:across\:AD=Potential\:across\:AF$

∴ They are considered to be in parallel. [AD || AF]

Similarly, BC || BE and CD || EF

See the attachment for better understanding! :)

★ Equivalent resistance b/w A & B :

$\sf:\implies\:\dfrac{1}{R_{AB}}=\dfrac{1}{R}+\dfrac{2}{3R}$

$\sf:\implies\:\dfrac{1}{R_{AB}}=\dfrac{3R+2R}{3R^2}$

$\sf:\implies\:\dfrac{1}{R_{AB}}=\dfrac{5}{3R}$

$:\implies\:\underline{\boxed{\bf{\orange{R_{AB}=\dfrac{3R}{5}\:\Omega}}}}$