Question

Calculate net resistance between A and B 

(A) (4r/5) 

(B) (5r/2) 

(C) 4r 

(D) (5r/4)

Answer 1

The correct option (A) (4r/5)  

Explanation:

The circuit can be drawn as shown in (a) in upper and lower hiangle, two r are in series. This series combination in parallel to r. Hence Reff = r || (r + r)

= r || 2r = {(r × 2r)/(r + 2r)} = (2/3)r

Hence redrawing circuit as shown in (b). Now seen from figure (b),

 r, r, (2r/3) resistors are in series. Hence their equivalent resistance is r + r + (2r/3) = (8r/3)

Finally the combination is (8r/3) || 2r || (8r/3)

Hence    R_AB = {(8r/3) || 2r || (8r/3)}

= {(4r/3) || 2r}

= [{(4r/3) × 2r}/{(4r/3) + 2r}]

= [{(8/3)r²}/{10r/3}

= (8/10)r = (4/5)r