Question

In the network shown in the following adjacent Figure, calculate the equivalent resistance between the points.  

1. A and B
2. A and C

 

Answer 1

(a) R_s = r₁ + r₂ + r₃

R_s = 2 + 2 + 2

R_s = 6 Ω

`"R"_1` and `"R"_2` are connected in parallel 

`1/"R"=1/"R"_"s"+1/"r"_4 = 1/6 + 1/2 = 4/6 " i.e." 2/3` 

R = `3/2`

R = 1.5 Ω

(b) `"R"_("s"_1) = "r"_1 + "r"_2`

`"R"_("s"_1)` = 2 + 2 = 4 Ω

`"R"_("s"_2)` = r₃ + r₄ =  2 + 2 = 4 Ω

`"R"_1` and `"R"_2` are connected in parallel 

`1/"R" =1/"R"_("s"_1) + 1/"R"_("s"_2)`

`1/"R" = 1/4 + 1/4`

`1/"R" = 2/4 ~~ 1/2` 

R = 2 Ω