What is (a) the highest, (b) the lowest total resistance that can be secured 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_s + R_1 + R_2 +R_3 +R_4`
` = 4 + 8 + 12 +24 =48 Omega`
Thus, the highest resistance which can be secured is `48 Omega`.
( b )The lowest resistance can be secured by connecting all the four coils in parallel. In this case,
`1/R_p = 1/R_1 + 1/R_2 + 1/R_3 + 1/R_4`
`1/4 +1/8 +1/12 + 1/24`
`= (6 + 3 + 2 +1)/(24)`
` =12/24`
`:. R_p = 24/12`
`=2 Omega`
Thus, the lowest resistance which can be secured is `2Omega`.