Question

the effective capacitances of 2 capacitors in series is 1.6micro farad that in parallel is 10micro farad . the capacitors are

Answer 1

$$\begin{gathered} \frac{1}{c_s}=\frac{1}{c_1}+\frac{1}{c_2} \\ \frac{1}{c_s}=\frac{c_1+c_2}{c_1{c}_2}=\frac{5}{8} \end{gathered}$$--------(i)
c₁+c₂= 10 $\mu f$---------------(ii)
By putting the value of ii in (i) we get
$$\begin{gathered} \frac{10}{c_1{c}_2}=\frac{5}{8}=c_1{c}_2=16=c_1(10-c_1)=16 \\ {c_1}^2-10c_1+16=0 \\ {c_1}^2-8c_1-2c_1+16=0 \\ {c}_1(c_1-8)-2(c_1-8)=0 \\ {c}_1=8\mu f,c_2=2\mu f \end{gathered}$$