Charging and Discharging Capacitors

Equipment

• Electrolytic capacitor: Stores and releases electrical energy.
• Resistor: Used to control the charging and discharging rate.
• Battery: Provides a constant voltage for charging the capacitor.
• Voltmeter: Measures the voltage across the capacitor.
• Switch: Allows control of the current flow to charge or discharge the capacitor.

Part 1: Discharging the Capacitor

Graphs and Calculations

1. Log-Linear Plot:

• Calculate the natural logarithm of each voltage reading $\ln(V)$.
• Plot a graph of $\ln(V)$ against time $t$. This should yield a straight line with a negative gradient.

2. Determine Time Constant:

• For discharging, the voltage $V$ decays according to:

$$V = V_0 e^{-\frac{t}{RC}}$$

• Rearranging gives $\ln(V) = -\frac{1}{RC}t + \ln(V_0)$, showing that the gradient of the line is $-\frac{1}{RC}$.
• Use the gradient to find the time constant $RC$, where $\tau = RC$.

Part 2: Charging the Capacitor

Graphs and Calculations

1. Plot Voltage vs. Time:

• Plot a graph of voltage $V$ against time $t$, which should show an exponential growth curve.

2. Determine Time Constant:

• For charging, the voltage $V$ builds up as:

$$V = V_0 \left(1 - e^{-\frac{t}{RC}}\right)$$

• The time constant $RC$ can be determined by finding the time at which the voltage reaches approximately 63% of the maximum voltage $V_0$.

Improvements and Notes

1. Use a Data Logger:

• A data logger can improve timing accuracy and capture data more precisely than manual readings.

2. Consistent Battery Voltage:

• Ensure the battery remains at a consistent voltage throughout the experiment, as voltage drops can affect results.