Lesson Plan

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Lesson Plan
Grade: Date: 25/02/2026
Subject: Physics
Lesson Topic: use equations of the form x = x0 e–(t / RC) where x could represent current, charge or potential difference for a capacitor discharging through a resistor
Learning Objective/s:
  • Describe the exponential decay of charge, voltage, and current in a discharging capacitor.
  • Derive the decay equation x = x₀ e⁻ᵗ/RC using Kirchhoff’s loop rule and calculus.
  • Calculate the time constant τ = RC and predict the capacitor voltage after a given time.
  • Analyse how the time constant determines the rate of discharge and identify common errors.
Materials Needed:
  • Projector or interactive whiteboard
  • Slide deck with circuit diagram and equations
  • Capacitor‑resistor circuit kit or simulation software (e.g., PhET)
  • Worksheets with guided derivation and practice problems
  • Calculator (or graphing calculator)
  • Ruler/graph paper for sketching exponential curves
 Introduction:

Begin with a quick question: “What happens to a charged capacitor when it’s connected to a resistor?” Students recall Kirchhoff’s loop rule and basic capacitor concepts. Explain that today they will use the exponential decay formula to model this process, and they will be able to predict voltage at any time and explain the meaning of the time constant.
Lesson Structure:
  1. Do‑now (5 min): short recall quiz on Kirchhoff’s loop rule and capacitor basics.
  2. Mini‑lecture (10 min): introduce the discharge circuit, derive x = x₀ e⁻ᵗ/RC step‑by‑step, emphasizing I = ‑dQ/dt.
  3. Guided practice (12 min): work through the provided example, calculate τ and V(t) together.
  4. Simulation activity (10 min): students use a virtual RC circuit to vary R and C, observe the exponential curve, and record τ values.
  5. Check for understanding (8 min): exit‑ticket – write the voltage expression and explain the physical meaning of τ = RC.
  6. Homework briefing (5 min): assign three discharge problems, including one requiring a sketch of V(t) over 5τ.
Conclusion:

We revisited how the exponential decay equation x = x₀ e⁻ᵗ/RC describes capacitor discharge and why the time constant τ = RC sets the speed of that decay. Students demonstrated understanding through the simulation and exit‑ticket explanation. For homework, they will solve additional discharge problems and sketch the voltage curve over five time constants to reinforce the concept.