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Question

Physics Question on Combination of capacitors

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?10−9C3 ? 10^{-9}C

B

2?10−9C2 ? 10^{-9}C

C

2.5?10−9C2.5 ? 10^{-9}C

D

3.5?10−9C3.5 ? 10^{-9}C

Answer

2?10−9C2 ? 10^{-9}C

Explanation

Solution

In series combination of capacitors, charges on both capacitors will be same.
Vs=QC1+QC2V_s=\frac{Q}{C_1}+\frac{Q}{C_2}
⇒1000=Q(1C1+1C2)\Rightarrow 1000=Q\bigg(\frac{1}{C_1}+\frac{1}{C_2}\bigg)
⇒1000=Q(C1+C2C1C2)\Rightarrow 1000=Q\bigg(\frac{C_1+C_2}{C_1C_2} \bigg)
⇒Q=1000?C1C2C1+C2\Rightarrow Q=\frac{1000 ?C_1C_2}{C_1+C_2}
Q=1000?3?10−12?6?10−12(3+6)?10−12=189?10−9Q=1000 ?\frac{3 ?10^{-12}?6?10^{-12}}{(3+6)?10^{-12}}=\frac{18}{9}? 10^{-9}
=2?10−9C=2 ?10^{-9}C