Vernier Software & Technology

# Capacitors

## Introduction

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

$V(t) = V_{0}e^{-\frac{t}{RC}}$

The rate of the decrease is determined by the product RC, known as the time constant of the circuit. A large time 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

$V(t) = V_{0} \left( 1-e^{-\frac{t}{RC}} \right)$

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.

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

## Physics with Vernier

See other experiments from the lab book.

 1 Graph Matching 2A Back and Forth Motion 2B Back and Forth Motion 3A Cart on a Ramp 3B Cart on a Ramp 4A Determining g on an Incline 4B Determining g on an Incline 5 Picket Fence Free Fall 6 Ball Toss 7 Bungee Jump Accelerations 8A Projectile Motion (Photogates) 8B Projectile Motion (Projectile Launcher) 9 Newton's Second Law 10 Atwood's Machine 11 Newton's Third Law 12 Static and Kinetic Friction 13 Air Resistance 14 Pendulum Periods 15 Simple Harmonic Motion 16 Energy of a Tossed Ball 17 Energy in Simple Harmonic Motion 18A Momentum, Energy and Collisions 18B Momentum, Energy and Collisions 19A Impulse and Momentum 19B Impulse and Momentum 20 Centripetal Accelerations on a Turntable 21 Accelerations in the Real World 22 Ohm's Law 23 Series and Parallel Circuits 24 Capacitors 25 The Magnetic Field in a Coil 26 The Magnetic Field in a Slinky 27 Electrical Energy 28A Polarization of Light 28B Polarization of Light (Rotary Motion Sensor) 29 Light, Brightness and Distance 30 Newton's Law of Cooling 31 The Magnetic Field of a Permanent Magnet 32 Sound Waves and Beats 33 Speed of Sound 34 Tones, Vowels and Telephones 35 Mathematics of Music

### Experiment 24 from Physics with Vernier Lab Book

#### Included in the Lab Book

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