Question

Thirteen resistances each of resistance R $\Omega$ are connected in the circuit as shown in the figure. The effective resistance between A and B is?

• A. $\frac{4R}{3}\Omega$
• B. $2R\Omega$
• C. $R\Omega$
• D. $\frac{2R}{3}\Omega$

Answer 1

The correct option is D $\frac{2R}{3}\Omega$

The potential difference across the central resistor is zero due to symmetry of the circuit.

The circuit can be treated like a balance wheat stone bridge with all the resistors

being the equivalent resistor of the small triangle configuration at the four corners.

Thus, the effective resistance is same as the resistance of a single unit triangle shaped

resistance.

Hence, effective resistance $=\frac{(R+R)\times \left(R\right)}{(R+R)+R)}=\frac{2R}{3}$