Question

Four capacitors are connected to a battery as shown in figure. The ratio of charges on capacitors \(C_2\) and \(C_4\) is

• A. \(\frac{1}{14}\)
• B. \(\frac{3}{22}\)
• C. \(\frac{2}{9}\)
• D. \(\frac{4}{13}\)

Hint:

Find the series equivalent of C1, C2, C3 across V for the charge on C2, and use Q = CV for C4.

Answer 1

The Correct Option is B

Step 1: Identify the branches:
Branch 1 has C1, C2, C3 in series. Branch 2 is C4 alone. They are in parallel across V, so both branches have voltage V.

Step 2: Charge on branch 1:
The equivalent capacitance of branch 1 is $\left(\frac1C + \frac1{2C} + \frac1{3C}\right)^{-1} = \frac{6C}{11}$. Its charge is $\frac{6C}{11}V$, and this same charge sits on C2.

Step 3: Charge on C4:
$Q_4 = (4C)V$.

Step 4: Divide:
$\frac{Q_2}{Q_4} = \frac{6/11}{4} = \frac{6}{44} = \frac{3}{22}$.

Final Answer:
The ratio is 3/22. \[ \boxed{\frac{3}{22}} \]