Question

Three capacitors \(C_1 = 2 \mu \text F, ~C_2 = 6 \mu\text F ~\text{and}~ C_3 = 12 \mu\text F\) are connected as shown in figure. Find the ratio of the charges on capacitors \(C_1, ~C_2 ~\text{and}~ C_3\) respectively

• A. $1:2:2$
• B. $2:3:3$
• C. $2:1:1$
• D. $3:4:4$

Answer 1

The correct option is A $1:2:2$

Given that,
$C_1=2\mu \text{F},C_2=6\mu \text{F}\text{and}{C}_3=12\mu \text{F}$

As $C_1$ is connected to the battery, change on it is $q_1=C_{1}V=2V$

As $C_2\&C_3$ are in series, charge is equal on both the capacitors.
Effective capacitance for this series combination is $C_{eff}=\frac{C_2{C}_3}{C_2+C_3}=4\mu \text{F}$

Charge on $C_2\&C_3$ is $q_2=q_3=C_{eff}V=4V$

Hence ratio of charges is $q_1:q_2:q_3=1:2:2$