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
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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The two capacitors in the arms are in series and this branch is in parallel with the third capacitor across the battery.
Updated On: Nov 13, 2026
- 1.5
- 2.5
- 3.5
- 4.5
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept
From the figure, \(C_1\) and \(C_2\) are in series with each other, and this series branch is in parallel with \(C_3\). The battery voltage \(V\) appears across both branches.
Step 2: Series branch
\(C_{s}=\dfrac{C_1C_2}{C_1+C_2}=\dfrac{1C\times 2C}{3C}=\dfrac{2C}{3}\)
Charge on \(C_1\): \(Q_1=C_{s}V=\dfrac{2}{3}CV\).
Step 3: Parallel capacitor
\(C_3\) has the full voltage \(V\), so \(Q_3=3CV\).
Step 4: Calculation
\(\dfrac{Q_3}{Q_1}=\dfrac{3CV}{(2/3)CV}=\dfrac{9}{2}=4.5\)
Final Answer:
The ratio of the charges is 4.5. \[ \boxed{\text{(D) }4.5} \]
From the figure, \(C_1\) and \(C_2\) are in series with each other, and this series branch is in parallel with \(C_3\). The battery voltage \(V\) appears across both branches.
Step 2: Series branch
\(C_{s}=\dfrac{C_1C_2}{C_1+C_2}=\dfrac{1C\times 2C}{3C}=\dfrac{2C}{3}\)
Charge on \(C_1\): \(Q_1=C_{s}V=\dfrac{2}{3}CV\).
Step 3: Parallel capacitor
\(C_3\) has the full voltage \(V\), so \(Q_3=3CV\).
Step 4: Calculation
\(\dfrac{Q_3}{Q_1}=\dfrac{3CV}{(2/3)CV}=\dfrac{9}{2}=4.5\)
Final Answer:
The ratio of the charges is 4.5. \[ \boxed{\text{(D) }4.5} \]
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