Question

The effective resistance between point $\text{P}$ and $\text{Q}$ of the given electrical circuit shown is ?

• A. $\frac{2Rr}{R+r}$
  
• B. $\frac{8R(R+r)}{3R+r}$
  
• C. $2r+4R$
  
• D. $\frac{5R}{2}+2r$
  

Answer 1

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


The given circuit is symmetrical about the axis $\text{P}OQ$.

All junction lying on the $\perp$ drawn to the axis of symmetry are of equal potential. Hence, the circuit elements between equal potential points can be ignored.

Therefore, the given circuit can be redrawn as follows,


The equivalent resistance of the given circuit is,

$\frac{1}{R_{PQ}}=\frac{1}{4R}+\frac{1}{4R}+\frac{1}{2r}=\frac{4(R+r)}{8Rr}$

$\therefore R_{PQ}=\frac{2Rr}{R+r}$

Hence, option $\left(a\right)$ is the correct answer.

Key concept : Line of symmetry If line $\text{P}Q$ is the axis of symmetry of the given circuit, then all the junctions lying on $\perp$ drawn to the line $PQ$ will be of equal potential.