THE PRACTICE STUDIO
Go slowly. Ask why. Make it yours.
PRACTICE / Capacitor energy
Energy in a charged capacitor
A 4 μF capacitor is held at 10 V.
Find its stored energy.
Organize the givens & assumptions
- C = 4×10⁻⁶ F
- V = 10 V
Ideal linear capacitor; stated voltage is across its plates; neglect fringing and leakage.
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Problem: Energy in a charged capacitor
A 4 μF capacitor is held at 10 V.
Question: Find its stored energy.
Givens:
- C = 4×10⁻⁶ F
- V = 10 V
Assumptions: Ideal linear capacitor; stated voltage is across its plates; neglect fringing and leakage.
Choices (LaTeX):
A. 400\ \mathrm{\mu J}
B. 40\ \mathrm{\mu J}
C. 20\ \mathrm{\mu J}
D. 200\ \mathrm{\mu J}
Ask for my approach first. Help me distinguish a physical misconception from an algebra error without revealing which choice is correct.
Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.Start with the smallest hint.
Work through it with me.
One decision at a time. Pause, predict, then unpack the algebra.
The voltage is squared; capacitance times voltage alone gives charge, not energy.
Choose a physical relation
Charging work grows as the plate voltage rises, giving half the final charge-voltage product.
Why is this step valid?
Adding a small charge dq costs work V dq. Since V = q/C rises linearly from zero to its final value, the area under the voltage–charge graph is a triangle, not a rectangle.
Put capacitance in SI units
Use 4 × 10⁻⁶ F for the capacitance and square the full 10 V potential difference.
Why is this step valid?
Convert microfarads to farads and square the voltage to get energy in joules.
Substitute and interpret
Stored energy is 200 μJ; capacitance times voltage alone would give charge instead of energy.
Using charge and voltage gives the same stored energy.
TRY THE IDEA AGAIN
At the same voltage, double capacitance. What happens to stored energy?
YOUR LEARNING NOTE
How does this idea feel now?
Confidence is a reflection, not proof of mastery.
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