# Capacitors

## Introduction

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

$V = \frac{q} {C}$

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

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

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.

## Sensors and Equipment

This experiment requires each of the following Vernier sensors and equipment (unless otherwise noted):

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

The student-version preview includes:

• Step-by-step instructions for computer-based data collection
• List of materials and equipment

Note: The experiment preview of the computer edition does not include essential teacher information, safety tips, or sample data. Instructions for Logger Pro and other software (such as LabQuest App or TI handheld software, where available) are on the CD that accompanies the book. We strongly recommend that you purchase the book before performing experiments.

## Standards Correlations

See all standards correlations for Science with TI-Nspire Technology »

## Experiment 31 from Science with TI-Nspire Technology Lab Book

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#### Included in the Lab Book

Vernier lab books include a CD with word-processing files of the student instructions, essential teacher information, suggested answers, sample data and graphs, and more.

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