Effective capacitance of parallel combination of two capacitors C 1 and C 2 is 10 μ F . When these…

1. $4.2\mathrm{\mu }\mathrm{F}$
2. $3.2\mathrm{\mu }\mathrm{F}$
3. $1.6\mathrm{\mu }\mathrm{F}$
4. $8.4\mathrm{\mu }\mathrm{F}$

Solution

Given $C_1+C_2=10\mu F\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}$ ...(i)
$4\left(\frac{1}{2}{C}_1{V}^2\right)=\frac{1}{2}{C}_2{V}^2$
$\Rightarrow \hspace{0.17em}\hspace{0.17em}4C_1=C_2$...(ii)
From equation (i) and (ii)
$C_1=2\mu F$
$C_2=8\mu F$
If they are in series
$\mathrm{}{C}_{eq}=\frac{C_1{C}_2}{C_1{+}_2}=1.6\mu F$

Asked in: JEE Main 2020 (08 Jan Shift 1)

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