Question:
Three capacitors \(C_1\), \(C_2\) and \(C_3\) are connected to voltage source V as shown in figure. The voltage across \(C_3\) will be
Three capacitors \(C_1\), \(C_2\) and \(C_3\) are connected to voltage source V as shown in figure. The voltage across \(C_3\) will be
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\(C_1\) and \(C_2\) are in parallel, and that pair is in series with \(C_3\) and the source.
Updated On: Oct 1, 2026
- \(\frac{C_3V}{(C_1+C_2+C_3)}\)
- \(\frac{(C_1+C_2)V}{C_3}\)
- \(\frac{(C_2+C_3)V}{C_1+C_2}\)
- \(\frac{(C_1+C_2)V}{(C_1+C_2+C_3)}\)
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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 connected in parallel, and this combination is in series with \(C_3\) and the battery \(V\).
Step 2: Key Formula or Approach
Parallel pair: \(C_{12}=C_1+C_2\). In a series chain, all capacitors hold the same charge \(Q\) and the voltage divides inversely with capacitance.
Step 3: Detailed Explanation
\[ C_{eq}=\frac{(C_1+C_2)C_3}{C_1+C_2+C_3},\quad Q=C_{eq}V \]
\[ V_3=\frac{Q}{C_3}=\frac{(C_1+C_2)V}{C_1+C_2+C_3} \]
Final Answer:
The voltage across \(C_3\) is \(\frac{(C_1+C_2)V}{C_1+C_2+C_3}\), option (D). \[ \boxed{\dfrac{(C_1+C_2)V}{C_1+C_2+C_3}\ \text{(D)}} \]
From the figure, \(C_1\) and \(C_2\) are connected in parallel, and this combination is in series with \(C_3\) and the battery \(V\).
Step 2: Key Formula or Approach
Parallel pair: \(C_{12}=C_1+C_2\). In a series chain, all capacitors hold the same charge \(Q\) and the voltage divides inversely with capacitance.
Step 3: Detailed Explanation
\[ C_{eq}=\frac{(C_1+C_2)C_3}{C_1+C_2+C_3},\quad Q=C_{eq}V \]
\[ V_3=\frac{Q}{C_3}=\frac{(C_1+C_2)V}{C_1+C_2+C_3} \]
Final Answer:
The voltage across \(C_3\) is \(\frac{(C_1+C_2)V}{C_1+C_2+C_3}\), option (D). \[ \boxed{\dfrac{(C_1+C_2)V}{C_1+C_2+C_3}\ \text{(D)}} \]
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