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 A and C is

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

Answer 1

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

To calculate the effective resistance between A and C, connect a battery across A and C as shown.
Points E and F are symmeteric to AC and both are connected to A and C by single resistor of equal resistance. Hence points E and F will be at same potential when connected to the battery.
Since E and F are equipotential points, therefore no current will flow across ED, EB, DF and BF and hence resistor connected across them can be neglected. The circuit diagram can be redrawn as shown below.
As it can be seen in the circuit diagram that A and C are connected by four branches each having two resistor of equal resistance($R$) connected in series. Hence each branch will have equivalent resistance $2R$. Hence circuit diagram can be redrawn as shown.
Therefore the equivalent resistance across A and C will be,
$\frac{1}{R_{AC}}=4\times \frac{1}{2R}$
$R_{AC}=\frac{R}{2}$