Question

The series combination of two capacitors shown in figure is connected across 1000V. The magnitude of the charges on the capacitors will be

• A. $3\times 10^{-9}C$
• B. $2\times 10^{-9}C$
• C. $2.5\times 10^{-9}C$
• D. $3.5\times 10^{-9}C$

Answer 1

Answer: (B)

In series combination of capacitors, charges on both capacitors will be same.
$V_s=\frac{Q}{C_1}+\frac{Q}{C_2}$
$\Rightarrow 1000=Q(\frac{1}{C_1}+\frac{1}{C_2})$
$\Rightarrow 1000=Q\left(\frac{C_1+C_2}{C_1{C}_2}\right)$
$\Rightarrow Q=\frac{1000\times C_1{C}_2}{C_1+C_2}$
$Q=1000\times \frac{3\times 10^{-12}\times 6\times 10^{-12}}{(3+6)\times 10^{-12}}=\frac{18}{9}\times 10^{-9}$
$=2\times 10^{-9}C$