What is : (a) the highest (b) the lowest total resistances that can be obtained by combinations of four coils of resistances `4 Omega,8 Omega,12 Omega,24 Omega` ?

Explanation

(a) The highest resistance can be secured (or obtained) by connecting all the four coils in series. In this case:
`R = R_(1) +R_(2)+R_(3)+R_(4)`
`R = 4+ 8 +12 +24`
`R = 48 Omega`
Thus, the highest resistance which can be secured is 48 ohms.
(b) The lowest resistance can be secured by connecting all the four coils in parallel. In this case:
`(1)/(R) = (1)/(R_(1)) +(1)/(R_(2))+(1)/(R_(3)) + (1)/(R_(4))`
`(1)/(R) = (1)/(4) +(1)/(8) +(1)/(12) +(1)/(24)`
`(1)/(R) = (6+3+2+1)/(24)`
`(1)/(R) = (12)/(24)`
`(1)/(R) = (1)/(2)`
`R = 2 Omega`
Thus, the lowest resistance which can be secured is 2 ohms.