Question:
A capacitor of capacitance C has charge Q and energy stored in it is W. If the charge is increased to 3Q, the energy stored in the capacitor W' will be
A capacitor of capacitance C has charge Q and energy stored in it is W. If the charge is increased to 3Q, the energy stored in the capacitor W' will be
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Energy in terms of charge is Q squared over 2C.
Updated On: Oct 1, 2026
- \(9W\)
- \(3W\)
- \(\frac{W}{3}\)
- \(\frac{W}{6}\)
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
The energy stored in a capacitor is \(W = \frac{Q^2}{2C}\). With \(C\) fixed, \(W\) is proportional to \(Q^2\).
Step 2: Key Formula or Approach:
New charge \(= 3Q\).
Step 3: Detailed Explanation:
\[ W' = \frac{(3Q)^2}{2C} = 9\cdot\frac{Q^2}{2C} = 9W \]
Option B, \(3W\), would be the result if energy were proportional to \(Q\), which is not so.
Since the capacitance \(C\) does not change, energy depends on charge alone. A common slip is to treat energy as proportional to \(Q\) (giving \(3W\)), but energy is quadratic in \(Q\), so tripling the charge gives nine times the energy.
Final Answer:
The new energy is \(9W\), option (A). \[ \boxed{9W} \]
The energy stored in a capacitor is \(W = \frac{Q^2}{2C}\). With \(C\) fixed, \(W\) is proportional to \(Q^2\).
Step 2: Key Formula or Approach:
New charge \(= 3Q\).
Step 3: Detailed Explanation:
\[ W' = \frac{(3Q)^2}{2C} = 9\cdot\frac{Q^2}{2C} = 9W \]
Option B, \(3W\), would be the result if energy were proportional to \(Q\), which is not so.
Since the capacitance \(C\) does not change, energy depends on charge alone. A common slip is to treat energy as proportional to \(Q\) (giving \(3W\)), but energy is quadratic in \(Q\), so tripling the charge gives nine times the energy.
Final Answer:
The new energy is \(9W\), option (A). \[ \boxed{9W} \]
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