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

Answer 1

Answer: (B)

In series combination of capacitors, charges on both capacitors will be same.
$V_s=\frac{Q}{C_1}+\frac{Q}{C_2}$
$\Rightarrow 1000=Q\bigg(\frac{1}{C_1}+\frac{1}{C_2}\bigg)$
$\Rightarrow 1000=Q\bigg(\frac{C_1+C_2}{C_1C_2} \bigg)$
$\Rightarrow Q=\frac{1000 ×C_1C_2}{C_1+C_2} $
$Q=1000 ×\frac{3 ×10^{-12}×6×10^{-12}}{(3+6)×10^{-12}}=\frac{18}{9}× 10^{-9}$
$=2 ×10^{-9}C$