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If the charge on a capacitor is doubled, what happens to the energy stored? (201

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Question: If the charge on a capacitor is doubled, what happens to the energy stored? (2019)

Options:

  1. It remains the same
  2. It doubles
  3. It quadruples
  4. It halves

Correct Answer: It quadruples

Exam Year: 2019

Solution: 

The energy stored in a capacitor is proportional to the square of the charge (U = Q^2/(2C)). Doubling the charge increases the energy by a factor of 4.

If the charge on a capacitor is doubled, what happens to the energy stored? (201

Practice Questions

Q1
If the charge on a capacitor is doubled, what happens to the energy stored? (2019)
  1. It remains the same
  2. It doubles
  3. It quadruples
  4. It halves

Questions & Step-by-Step Solutions

If the charge on a capacitor is doubled, what happens to the energy stored? (2019)
  • Step 1: Understand that a capacitor stores energy based on its charge.
  • Step 2: Know the formula for energy stored in a capacitor: U = Q^2 / (2C), where U is energy, Q is charge, and C is capacitance.
  • Step 3: If the charge (Q) is doubled, it becomes 2Q.
  • Step 4: Substitute 2Q into the energy formula: U = (2Q)^2 / (2C).
  • Step 5: Calculate (2Q)^2, which equals 4Q^2.
  • Step 6: Now the formula looks like this: U = 4Q^2 / (2C).
  • Step 7: Simplify the equation: U = 2Q^2 / C.
  • Step 8: Compare the new energy (2Q^2 / C) to the original energy (Q^2 / (2C)).
  • Step 9: Notice that the new energy is 4 times the original energy.
  • Step 10: Conclude that doubling the charge increases the energy stored by a factor of 4.
  • Energy Stored in a Capacitor – The energy (U) stored in a capacitor is given by the formula U = Q^2/(2C), where Q is the charge and C is the capacitance.
  • Proportional Relationships – Understanding how changes in charge affect energy, specifically that energy is proportional to the square of the charge.
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