# Capacitors

Recommended for High School.

## Introduction

The charge *q* on a capacitor’s plate is proportional to the potential difference V across the capacitor. We express this relationship 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 *V*_{0} (volts) is connected across a resistor *R* (in ohms), a time-dependent current will flow according to Ohm’s law. This situation is shown by the RC (resistor-capacitor) circuit below when the switch is connecting terminals 33 and 34.

As the charge flows, the charge *q* on the capacitor 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 constant means that the capacitor will discharge slowly.

In contrast, when the capacitor is charged, the potential across it approaches the final value exponentially, modeled by

The same time constant, RC, describes the rate of charging as well as discharging.

## 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 and as it charges.
- Fit an exponential function to the data. One of the fit parameters corresponds to an experimental time constant.

## Sensors and Equipment

This experiment features the following Vernier sensors and equipment.

### Additional Requirements

You may also need an interface and software for data collection. What do I need for data collection?