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 and 24 Omega`?

Explanation

a) To obtain highest resistance, all the four resistances must be connected in series arrangement.
In that case resultant resistance `R_s` is given by
`R_s=R_1+R_2+R_3+R_4=4+8+12+24=48 Omega`
(b) To obtain lowest resistance, all the four resistances must be connected in parallel arrangement, in that case the resultant resistance `R_p` is given by :
`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 Omega =2 Omega`