Question 444: Electrostats & Capacitance

Question

Three capacitors are connected to a battery as shown in figure. The ratio of charge on capacitors $\mathrm{C}_3$ and $\mathrm{C}_1$ is

Accepted Answer

Here, $C_1$ and $C_2$ are in series
$$ C_{12}=\frac{C_1 C_2}{C_1+C_2}=\frac{2 C^2}{3 C}=\frac{2}{3} C $$
Also, $C_3$ is parallel to $C_1$ and $C_2$
$$ 	herefore  C_{e q}=C_{12}+C_3=\frac{2}{3} C+3 C=\frac{11}{3} C $$
Charge on capacitor $\mathrm{C}_3$
$$ Q_3=C_3 \cdot V=3 C V $$
Charge on capacitor $\mathrm{C}_1$
$$ \begin{aligned} &	ext { In series, charge on } C_1=Q_1=Q_{12}\ &\begin{aligned} & \mathrm{Q}_{12}=\mathrm{C}_{12} \mathrm{~V}=\frac{2}{3} \mathrm{CV} \ 	herefore \quad & \frac{	ext { Charge on } \mathrm{C}_3}{	ext { Charge on } \mathrm{C}_1}=\frac{3 \mathrm{CV}}{\frac{2}{3} \mathrm{CV}}=\frac{9}{2}=4.5 \end{aligned} \end{aligned} $$

Answer

1.5

Answer

2.5

Answer

3.5

Answer

4.5

Electrostats & Capacitance

Three capacitors are connected to a battery as shown in figure. The ratio of charge on capacitors \mathrm{C}_3 and \mathrm{C}_1 is

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