The equivalent capacitance of the parallel and the series combinations of two capacitors are `5mu F " and " 1.2 muF`, respectively. Calculate the capacitances of each capacitor.

Explanation

Let the capacitors of the two capacitors be `C_1muF" and "C_2muF`. According to the question,
`C_1+C_2=5" ""…………….."(1)`
and `(C_1C_2)/(C_1+C_2)= 1.2`
or, `C_1C_2= 1.2xx5 =6" ""…………….."(2)`
or, `C_1(5-C_1)-6=0 " "[" with the help of equation "(1)]`
or, `C_1^2-5C_1+6=0 " or "(C_1-3)(C_1-2)=0`
`:. C_1=3 " or "2`
If `C_1=3, C_2=5-3=2`
and if `C_1=2, C_2= 5-2=3`
So, the capacitances of the two capacitors are `3muF " and "2 muF`.