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A parallel plate capacitor has a capacitance of 5 µF. If the potential differenc

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Question: A parallel plate capacitor has a capacitance of 5 µF. If the potential difference across it is increased from 10 V to 20 V, what is the change in stored energy?

Options:

  1. 25 µJ
  2. 50 µJ
  3. 75 µJ
  4. 100 µJ

Correct Answer: 50 µJ

Solution: 

Energy U = 1/2 C V^2. Initial U = 1/2 * 5 × 10^-6 * 10^2 = 0.025 J; Final U = 1/2 * 5 × 10^-6 * 20^2 = 0.1 J. Change = 0.1 - 0.025 = 0.075 J = 75 µJ.

A parallel plate capacitor has a capacitance of 5 µF. If the potential differenc

Practice Questions

Q1
A parallel plate capacitor has a capacitance of 5 µF. If the potential difference across it is increased from 10 V to 20 V, what is the change in stored energy?
  1. 25 µJ
  2. 50 µJ
  3. 75 µJ
  4. 100 µJ

Questions & Step-by-Step Solutions

A parallel plate capacitor has a capacitance of 5 µF. If the potential difference across it is increased from 10 V to 20 V, what is the change in stored energy?
  • Step 1: Identify the formula for the energy stored in a capacitor, which is U = 1/2 C V^2.
  • Step 2: Note the given values: capacitance C = 5 µF (which is 5 × 10^-6 F) and initial voltage V1 = 10 V.
  • Step 3: Calculate the initial energy (U1) using the formula: U1 = 1/2 * C * V1^2.
  • Step 4: Substitute the values into the formula: U1 = 1/2 * 5 × 10^-6 * (10)^2.
  • Step 5: Calculate U1: U1 = 1/2 * 5 × 10^-6 * 100 = 0.025 J.
  • Step 6: Now, note the final voltage V2 = 20 V.
  • Step 7: Calculate the final energy (U2) using the same formula: U2 = 1/2 * C * V2^2.
  • Step 8: Substitute the values into the formula: U2 = 1/2 * 5 × 10^-6 * (20)^2.
  • Step 9: Calculate U2: U2 = 1/2 * 5 × 10^-6 * 400 = 0.1 J.
  • Step 10: Find the change in stored energy by subtracting the initial energy from the final energy: Change = U2 - U1.
  • Step 11: Substitute the values: Change = 0.1 J - 0.025 J.
  • Step 12: Calculate the change: Change = 0.075 J.
  • Step 13: Convert the change in energy to microjoules: 0.075 J = 75 µJ.
  • Capacitance and Energy Storage – Understanding how capacitance relates to energy stored in a capacitor, using the formula U = 1/2 C V^2.
  • Potential Difference – Recognizing the effect of changing the potential difference on the energy stored in a capacitor.
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