Core Practical 11: Investigating Capacitor Charge & Discharge
Exponential decay law arises from the balance between the instantaneous voltage across the capacitor and the resistor’s ohmic response. Solving the differential equation gives , demonstrating that discharge progresses more rapidly with smaller resistance or capacitance.
Natural logarithm linearisation is used to convert nonlinear exponential data into a straight-line relationship. Taking the logarithm of the decay equation yields , enabling determination of the time constant from the slope of the line.
Constant current–voltage relationship during discharge follows from Ohm’s law, ensuring that current also decays exponentially. Because voltage, current, and charge depend linearly on one another in a simple capacitor–resistor circuit, all share the same time constant.
Data collection during discharge involves charging the capacitor fully, switching it to discharge through a resistor, and recording the voltage at regular time intervals. Frequent sampling improves curve resolution and makes subsequent linearisation more reliable.
Plotting vs. provides a method to extract capacitance from experimental measurements. Once a line of best fit is drawn, the gradient equals , allowing calculation of when is known.
Ensuring accurate timing requires synchronising stopwatch readings with stable voltmeter measurements. Using slow discharge (large resistance) makes the decay easier to capture and reduces timing errors caused by reaction delays.
Check the mode (charging vs. discharging) by looking at the direction of voltage change. Correct interpretation ensures that initial conditions are applied properly in equations involving or .
Verify the gradient sign when analysing plots. A negative slope indicates exponential decay, and errors here lead directly to incorrect capacitance calculations.
Perform dimensional checks on derived expressions such as . Ensuring units of farads validates the algebra and flags common mistakes like sign reversal.
Links to RC circuits illustrate that capacitor discharge models general first-order differential systems, including cooling processes or radioactive decay. Recognising shared mathematical structure broadens transferability of knowledge.
Applications in filters and timing circuits show how the same exponential behaviour governs signal smoothing and delays in electronics. Understanding discharge dynamics supports deeper analysis of electronic design.
Extension to natural log methods highlights how linearisation techniques generalise to many scientific contexts, reinforcing graph-based parameter extraction skills.