Lesson Plan

• Describe the relationship between charge, voltage, and capacitance.
• Explain why the area under a V‑Q graph equals the stored electric potential energy.
• Calculate the energy stored in ideal and non‑linear capacitors using geometric or integral methods.
• Apply the appropriate formula (½ QV, ½ CV², or ∫V dQ) to solve practice problems.
• Identify common pitfalls such as using the wrong formula when capacitance varies.

• Projector and screen
• Whiteboard and markers
• Printed worksheet with V‑Q graphs
• Scientific calculators
• Graph paper and rulers
• Capacitor demonstration kit (variable and fixed capacitors)

Imagine charging a smartphone battery and wondering exactly how much energy is stored. Students already know Q = CV and basic integration, so we will connect that knowledge to a visual graph. By the end of the lesson they will be able to determine the stored energy from any V‑Q plot and explain the reasoning.

1. Do‑Now (5'): Quick quiz on Q = CV and units of energy.
2. Mini‑lecture (10'): Derive U = ∫V dQ and show the triangle area for an ideal capacitor.
3. Guided Example (12'): Work through the 5 µF – 200 V example, calculating Q and U.
4. Group Activity (15'): Students calculate energy for a non‑linear V‑Q relationship (V = kQ²) using integration.
5. Check for Understanding (5'): Exit‑ticket question – give a V‑Q graph and ask for the energy expression.
6. Summary (3'): Recap formulas and common errors.

We reviewed how the area under a V‑Q graph directly gives the stored energy and practiced both geometric and integral approaches. For homework, students will complete a worksheet with three new V‑Q graphs, including one with a piece‑wise linear curve. The exit ticket collected today will be used to gauge individual understanding.