What are [i] the highest and [ii] the lowest total resistances which can be secured by combinations of four coils of resistances `4Omega,8Omega,12Omegaand24Omega`?

Explanation

i] For highest resistance, resistors are connected in series. `R_(s)=R_(1)+R_(2)+R_(3)+R_(4)=4+8+12+24=48Omega`
ii] For lowest resistance, resistors are connected in parallel.
`1/R_(p)=1/4+1/8+1/12+1/24=(6+3+2+1)/24=12/24=1/2`.
Therefore, `R_(p)=2Omega`.