In the circuit elements given below, all individual resistors are identical. The resistance between P and Q in the different cases is

Options

A. a) `3R`
B. b) `5R//6`
C. c) `R//2`
D. d) R

Answer

b,c,d

Explanation

Here the resistance are is parallel their effective resistance is `R//3` Hence answer is wrong
(b) The effective resistance of first three resistance in parallel in `R//3` and next two resistance in parallel is `R//2`. Therefore the total resistance `= (R//3) + (R//2) = 5R//6`
(c) The upper tweo resistance and lower two resistance are in series .The effective resistance of each arm `= 2R` These two effective resistance
`= (2R xx 2R)/(2R + 2R) = R`. Now these two arms of resistance is in parallel with resistance `R` Hence effective resistance `P` and `Q`
`= (R xx R)/(R + R) = (R )/(2)`
(d) By symmtery the mid-joined `R` would not carry any current so effective resistance is only for `2R and 2R` parallel which will be `R`