Capacitors

Introduction

The charge q on a capacitor’s plate is proportional to the potential difference V across the capacitor. We express this with

where C is a proportionality constant known as the capacitance. C is measured in the unit of the farad, F, (1 farad = 1 coulomb/volt).

If a capacitor of capacitance C (in farads), initially charged to a potential V₀ (volts) is connected across a resistor R (in ohms), a time-dependent current will flow according to Ohm’s law. As the current flows, the charge q is depleted, reducing the potential across the capacitor, which in turn reduces the current. This process creates an exponentially decreasing current, modeled by

The rate of the decrease is determined by the product RC, known as the time constant of the circuit. A large time constantmeans that the capacitor will discharge slowly.

Objectives

• Measure an experimental time constant of a resistor-capacitor circuit.
• Compare the time constant to the value predicted from the component values of the resistance and capacitance.
• Measure the potential across a capacitor as a function of time as it discharges.
• Fit an exponential function to the data. One of the fit parameters corresponds to an experimental time constant.