Question 13 – Capacitors - OCR A A Level Physics Questions

A student wishes to determine the permittivity $ε\varepsilon$ of polythene using a capacitor made in the laboratory.

The capacitor consists of two large parallel aluminium plates separated by a very thin sheet of polythene.

The capacitor is initially charged to a potential difference $V_0$ using a battery. The capacitor is then discharged through a fixed resistor of resistance $MΩ2.0\text{ M}\Omega$ .

The potential difference $V$ across the capacitor after a time $t$ is recorded by a data-logger. The student uses the data to draw the $ln⁡(V/V)\ln(V/\text{V})$ against $t$ graph shown below.

$A grid showing a vertical axis labeled \ln(V/\text{V}) graded from 1.0 to 2.2 with grid lines every 0.02 units, and a horizontal axis labeled t/\text{ms} graded from 0 to 10 ms with grid lines every 0.2 ms. A straight line of negative slope starts at (0, 2.00) on the vertical axis and terminates at (10, 1.20) on the horizontal axis limit.$

Show that the magnitude of the gradient of the line shown in the graph is equal to

\frac{1}{CR}

where $C$ is the capacitance of the capacitor and $R$ is the resistance of the resistor.

Use the graph to determine the capacitance $C$ of the capacitor. Describe how the student can then use this value of $C$ to determine a value for the permittivity $ε\varepsilon$ of polythene. In your description, mention any additional measurements required on the capacitor.