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If the capacitance of a capacitor is doubled while keeping the charge constant,

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Question: If the capacitance of a capacitor is doubled while keeping the charge constant, what happens to the potential difference across it? (2020)

Options:

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

Correct Answer: It halves

Exam Year: 2020

Solution: 

Capacitance C is defined as C = Q/V. If C is doubled and Q remains constant, then V must halve to maintain the equation.

If the capacitance of a capacitor is doubled while keeping the charge constant,

Practice Questions

Q1
If the capacitance of a capacitor is doubled while keeping the charge constant, what happens to the potential difference across it? (2020)
  1. It doubles
  2. It halves
  3. It remains the same
  4. It quadruples

Questions & Step-by-Step Solutions

If the capacitance of a capacitor is doubled while keeping the charge constant, what happens to the potential difference across it? (2020)
  • Step 1: Understand the formula for capacitance, which is C = Q/V, where C is capacitance, Q is charge, and V is potential difference.
  • Step 2: Identify that in this scenario, the capacitance (C) is being doubled.
  • Step 3: Recognize that the charge (Q) remains constant throughout this process.
  • Step 4: Since C is doubled, we can write the new capacitance as 2C.
  • Step 5: Substitute the new capacitance into the formula: 2C = Q/V'. Here, V' is the new potential difference.
  • Step 6: Rearrange the equation to find V': V' = Q/(2C).
  • Step 7: Compare this with the original equation V = Q/C. Notice that V' is half of V.
  • Step 8: Conclude that if capacitance is doubled while keeping charge constant, the potential difference (V) must be halved.
  • Capacitance and Voltage Relationship – The relationship between capacitance (C), charge (Q), and potential difference (V) is defined by the formula C = Q/V, which shows how changes in capacitance affect voltage when charge is constant.
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