The equivalent resistance of two coils connected in series and in parallel are `12Omega` and `5/3 Omega` respectively. Calculate the value of each resistance.

Explanation

IF `R_1` and `R_2` be the two resistances, then equivalent resistance in series combination,
`R_1+R_2=12`………(1)
Equivalent resistance of parallel combination,
`(R_1R_2)/(R_1+R_2)=5/3or,(R_1R_2)/12=5/3or,R_1R_2=20`
Now, `(R_1+R_2)^2=(R_1+R_2)^2-4R_1R_2` =`12^2-4times20=144-80=64`
or, `R_1-R_2=8` [Here we assume `R_1 gt R_2`]..........(2)
Adding equations (1) and (2) we have
`2R_1=20 or,R_1=10 Omega`
From equation (1) we have,
`R_2=12-R_1=12-10=2Omega`