Question

Show how would you connect three resistors, each of resistance 6 O so that
the combination has a resistance of(a) 9 Ω (b) 4 .Ω

Answer 1

(a) To get an equivalent resistance of 9Ω using three 6 Ω resistors, they should be connected in parallel as shown:

Between A and C, the equivalent resistance is

`1/"R"_"parallel" = 1/6 + 1/6 = 2/6 = 1/3 Ω`

`"R"_"parallel" = 3 Ω

Between A and B, the equivalent resistance is
`"R"_"series" = 3 + 6 = 9Ω

(b) To get an equivalent resistance of 4 Ω using three 6 Ω resistors, they should be connected in parallel as shown:

 

Between A and B, the series combination of two 6 Ω resistors is connected in parallel with the third 6Ω resistor.

`"R"_"series" = 6 + 6 = 12Ω`

`1/"R"_"equivalent" = 1/6 + 1/12 = 3/12 = 1/4 Ω`