Question

Consider 12 resistors arranged symmetrically in shape of a bi - pyramid ABCDEF. Here, ABCD is a square. Point E, point F and center of the square are in the same straight line perpendicular to the plane of the square. The resistance of each resistor is $R$.
The effective resistance between E and F is

• A. $\frac{R}{2}$
• B. $\frac{R}{3}$
• C. $R$
• D. None of these

Answer 1

The correct option is A $\frac{R}{2}$

For calculating the equivalent resistance between E and F, lets connect a battery across E and F as shown.

Since points A, B, C and D are connected to E and F by resistor of equal resistance, therefore points A, B, C and D will be at same potential.
Since A, B, C and D are equipotential, therefore no current will flow across AB, BC, CD and DA. Hence the resistance across AB, BC, CD and DA can be neglected.
Hence the circuit can be redrawn as shown.
Its evident that E and F are connnected by 4 branches each of them having two resistors of equal resistance connected in series. Hence their equivalent will be $2R$ and the circuit can be redrawn as shown
Hence equivalent resistance across E and F,
$\frac{1}{R_{EF}}=4\times \frac{1}{2R}$
$R_{EF}=\frac{R}{2}$
Hence option A is correct.