Find the equivalent resistances of the networks shown in figure between the points a and b.

Q. Find the equivalent resistances of the networks shown in figure between the points a and b.

(a) (5/7) r Ω

(b) (5/8) r Ω

(c) (8/5) r Ω

(d) (7/5) r Ω

Ans: (b)

Sol: Diagonal resistor is in parallel with two resistors (which is in series = 2r)

hence , $ \displaystyle R’ = \frac{2r \times r}{2r + r} = \frac{2r}{3} $

Now 2r/3 is in series with r .

R” = r + 2r/3 = 5r/3

now , 5r/3 is in parallel with ab(=r)

$ \displaystyle R_{ab} = \frac{5r/3 \times r}{5r/3 + r} $

$ \displaystyle R_{ab} = \frac{5 r}{8} $