The effective resistance between points P and Q of the
electrical circuit shown in the figure is
(a) `(2Rr)/(R+r)`
(b)`(8R(R+r))/(3R +r)`
(c) `2r + 4R`
(d) `(5R)/2 + 2r` .
.

Options

A. `2 Rr // (R + r)`
B. `8R (R + r) // (3R + r)`
C. `2r + 4R`
D. `5R // 2 + 2r`

Answer

A

Explanation

(a)
In a circuit, any circuit element placed between points at the same potential can be removed, without affecting the rest of the circuit. Here, by symmetry, point `A, B` and `C` are at same potential, for any potential difference between `P` and `Q`
The circuit can therefore be reduced as shown below

Effective resistance `R_(eq) = (2 Rr)/(R + r)`.