Question

Thirteen resistance each of resistance R ohm 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 given circuit represents a Wheatstone bridge circuit.
The equivalent resistance of each arm is $R_a=R||(R+R)=\frac{R\times 2R}{R+2R}=\frac{2R}{3}$
As all arm resistances are same, so it is a balanced bridge.Thus we can removed the middle resistance R from the circuit.
The effective resistance between A and B is $R_{ab}=(2R/3+2R/3)||(2R/3+2R/3)=\left(4R/3\right)||\left(4R/3\right)=2R/3$