Question

Show how would you join three resistors, each of resistance 9 Ω so that the equivalent resistance of the combination is 

1) 13.5 

2) 6 Ω

Answer 1

1) Case: To get equivalent resistance = 13.5 Ω

For this case, two 9 Ω resistors should be first connected in parallel and then their combination should be connected in series with the remaining 9 Ω resistor. Thus,

`R = (9xx9)/(9+9) = 81/18` = 4.5 Ω

`R_"total"` = R + 9 = 4.5 + 9 = 13.5 Ω

2) Case: To get equivalent resistance = 6 Ω

For this case, two 9 Ω resistors should be first connected in series and then this combination should be connected in parallel with the remaining 9 Ω resistor. Thus,

R₁ = 9 + 9 = 18 Ω

`R_"total" = (R_1xxR)/(R_1+R) = (18xx9)/(18+9)` = 6 Ω