Figure shows charge (q) versus voltage (V) graph for series and parallel combination of two given capacitors. The capacitances are :
Correct Option: 1
(1) Equivalent capacitance in series combination (C') is given by
$\frac{1}{\mathrm{C}},=\frac{1}{\mathrm{C}_{1}}+\frac{1}{\mathrm{C}_{2}} \Rightarrow \mathrm{C}^{\prime}=\frac{\mathrm{C}_{1} \mathrm{C}_{2}}{\mathrm{C}_{1}+\mathrm{C}_{2}}$
For parallel combination equivalent capacitance $\mathrm{C}^{\prime \prime}=\mathrm{C}_{1}+\mathrm{C}_{2}$
For parallel combination
$\mathrm{q}=10\left(\mathrm{C}_{1}+\mathrm{C}_{2}\right)$
$\mathrm{q}_{1}=500 \mu \mathrm{C}$
$500=10\left(\mathrm{C}_{1}+\mathrm{C}_{2}\right)$
$\mathrm{C}_{1}+\mathrm{C}_{2}=50 \mu \mathrm{F}$ ....(1)
For Series Combination-
$\mathrm{q}_{2}=10 \frac{\mathrm{C}_{1} \mathrm{C}_{2}}{\left(\mathrm{C}_{1}+\mathrm{C}_{2}\right)}$
$80=10 \frac{C_{1} C_{2}}{50}$ From equation ....(2)
$\mathrm{C}_{1} \mathrm{C}_{2}=400$ ....(3)
From equation (i) and (ii)
$\mathrm{C}_{1}=10 \mu \mathrm{F} \quad \mathrm{C}_{2}=40 \mu \mathrm{F}$