Question

Six resistors of 3 ohm each are connected along the
sides of a hexagon and three resistors of 6 ohm each
are connected along AC, AD and AE as shown in the
figure. The equivalent resistance between A and B is equal to?
​

Answer 1

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HERE IS UR ANSWER

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Resistances RAF and RFE are in series combination.

Therefore their equivalent resistance R= RAF+ RFE = 3 + 3 = 6 Ω  .

Now the resistance RAE and equivalent resistance R' are in parallel combination.

Therefore relation for their equivalent resistance.

We can calculate in the same manner for RED, RAC, RDC. etc. and finally the circuit reduces as shown in the figure. 

Therefore, the equivalent resistance between A and B is

$\frac{(3 + 3) \times 3}{(3 + 3) + 3} = \frac{18}{9} = 2ohm$

Answer 2

$\sf\bold{{ }}Explanation: Résistance \: \sf\bold{{R_{(AF)} }} \: and \: \\ \sf\bold{{R_{(FE)} }} \: are \: in \: the \: series \: combination. \\ \sf\bold{{ }}Therefore \: their \: equivalent \: resistance, \: is \\ \sf\bold{{ }}R {}^{1} \: is \: given \: by$

$R {}^{1} = \sf\bold{\red{R_{(AF)} }} + \sf\bold{\red{R_{(FE)} }} </p><p>$

$R {}^{1} = 3 + 3$

$R {}^{1} = 6Ω$

$\sf\bold{\red{{} }}Now, the \: resistance \: \sf\bold{\red{R_{(AE)} }} and \: equivalent \\ \sf\bold{{{} }} Resistance \: R {}^{1} \: are \: in \: parallel \: combination. \\ \sf\bold{{{} }}Therefore \: their \: equivalent \: resistance \: R {}^{11} \\ \sf\bold{{{} }}is \: given \: by$

$\frac{1}{R {}^{11} } = \frac{1}{R {}^{1} } + \frac{1}{\sf\bold{{R_{(AE)} }}}$

$\frac{1}{R {}^{11} } = \frac{1}{6} + \frac{1}{6}$

$\frac{1}{R {}^{11} } = \frac{1}{3}$

$R {}^{11} = 3Ω$

$In \: same \: manner \: \sf\bold{\red{R_{(AD)} }} = 3Ω, \\ \sf\bold{\red{R_{(AC)} }} = 3 \: and \: Finally \: the \: equivalent \: \\ \sf\bold{\red{{} }}resistance \: between \: A \: and \: B \: is \: given \: by$

$\frac{1}{\sf\bold{\red{R_{(AB)} }}} = \frac{1}{6} + \frac{1}{3}$

$\frac{1}{\sf\bold{\red{R_{(AB)} }}} = \frac{1 + 2}{6}$

$\frac{1}{\sf\bold{\red{R_{(AB)} }}} = \frac{3}{6}$

$\frac{1}{\sf\bold{\red{R_{(AB)} }}} = \frac{1}{2}$

$\sf\bold{\red{R_{(AB)} }} = 2Ω$

Therefore, the equivalent Resistance between

A and B is 2Ω.