Capacitor Charge

Test yourself

Charging a Capacitor

When the capacitor is charging up, the formulae (and graphs) are different.

Voltage

The formula for this graph is:
- $V=V_0(1-e^{-\frac{t}{RC}})$
Where $V_0$ is the final potential difference across the capacitor.

Charge

The formula for this graph is:
- $Q=Q_0(1-e^{-\frac{t}{RC}})$
Where $Q_0$ is the final charge across the capacitor.

Charging and Discharging a Capacitor - Experiment

We can perform an experiment to test theoretical predications about capacitors.

Safety warning

Some capacitors, called electrolytic capacitors, respond badly (i.e. they can explode) if they are charged incorrectly.
It matters which way round the terminals of the capacitor are connected to the terminals of the power supply.
You must take care to construct charging circuits with the correct polarity.
In practice, small non-electrolytic capacitors are often given to students for this section to avoid this.

Set up

A circuit should be set up as in the diagram.

Method - charging

Start with a discharged capacitor and the switch in position 2.
Put the switch in position 1 and start the stopwatch simultaneously.
Record the voltmeter and ammeter readings frequently.
Stop the stopwatch once the p.d. has increased to about 95% of the EMF of the battery.

Method - discharging

Zero the stopwatch.
Start the stopwatch again, simultaneously switching the switch to position 2.
Record the voltmeter and ammeter readings frequently.
Stop the stopwatch once the p.d. has decreased to about 5% of the EMF of the battery.

Finding the time constant

The time constant is the time taken for the original p.d. to discharge to (1/e) times the original value.
- This happens at 37% of the original value.
The time constant can be found by reading the time from a V-t graph directly, or multiplying the gradient of a ln(V)-t graph by (-1).

Finding the capacitance

Once the time constant is calculated, the capacitance is the time constant divided by the resistance of the resistor.
- Capacitance (C) = time constant (RC) ÷ resistance (R).

Obtaining quality data

The challenge is to read and record the p.d. reading quickly enough because the reading can change rapidly.
The solution is to use a p.d. probe/digital voltmeter, connected to a datalogger and a computer.
The datalogger can take values of p.d. and time simultaneously, and without any reaction time issues connected with switching the switch and starting the stopwatch at the same time.

1Physical Quantities & Units

1.1Physical Quantities & Units

1.1.1Use of SI Units

1.1.2SI Prefixes, Standard Form & Converting Units

1.1.3End of Topic Test - Units & Prefixes

1.1.4Avogadro's Constant

1.1.5Scalars & Vectors

2Measurement Techniques

2.1Measurement, Errors & Uncertainty

2.1.1Measuring Length, Time & Volume

2.1.2Measuring Temperature

2.1.3Circuit Measurements

2.1.4Limitation of Physical Measurements

2.1.5Uncertainty

2.1.6Estimation

2.1.7Displaying Data

2.1.8End of Topic Test - Measurements & Errors

3Kinematics

3.1Equations of Motion

3.1.1Motion in a Straight Line

3.1.2Graphs of Motion

3.1.3Bouncing Ball Example

3.1.4End of Topic Test - Motion in a Straight Line

3.1.5Acceleration Due to Gravity

4Dynamics

4.1Momentum & Newton's Laws of Motion

4.1.1Mass & Inertia

4.1.2Newton's Laws

4.1.3Momentum

4.1.4End of Topic Test - Newton's Laws & Momentum

4.1.5A-A* (AO3/4) - Newton's Third Law

4.2Non-Uniform Motion

4.2.1Projectile Motion

4.3Linear Momentum & Conservation

4.3.1Conservation of Momentum

4.4Force, Density & Pressure

4.4.1Fields

4.4.2Force in Uniform Fields

4.4.3Friction

4.4.4Buoyancy

4.4.5Terminal Speed

4.4.6End of Topic Test - Acceleration Due to Gravity

4.4.7Centre of Mass

4.4.8Forces & Equilibrium

4.4.9End of Topic Test - Scalars & Vectors

4.4.10Moments

4.4.11End of Topic Test - Moments & Centre of Mass

4.4.12Density

4.4.13Pressure

4.5Work, Energy & Power

4.5.1Work & Energy

4.5.2Power & Efficiency

4.5.3Conservation of Energy

4.5.4End of Topic Test - Work, Energy & Power

4.6Circular Motion

4.6.1Circular Motion

4.6.2Circular Motion 2

4.6.3End of Topic Test - Circular Motion

5Gravitational Fields

5.1Gravitational Fields (A2 only)

5.1.1Newton's Law

5.1.2Gravitational Field Strength

5.1.3Gravitational Potential

6Deformation of Solids

6.1Materials

6.1.1Bulk Properties of Solids

6.1.2Energy in Materials

6.1.3Young Modulus

6.1.4End of Topic Test - Materials

7Thermal Physics

7.1Thermal Physics

7.1.1Temperature

7.1.2Measuring Temperature

7.1.3Ideal Gas Law

7.1.4Ideal Gases

7.1.5Boyle's Law & Charles' Law

7.1.6Molecular Kinetic Theory Model

7.1.7Molecular Kinetic Theory Model 2

7.1.8Thermal Energy Transfer

7.1.9Thermal Energy Transfer Experiments

7.1.10End of Topic Test - Thermal Energy & Ideal Gases

7.1.11First Law of Thermodynamics

8Oscillations

8.1Simple Harmonic Motion

8.1.1Simple Harmonic Motion

8.1.2Simple Harmonic Systems

8.1.3Energy in Simple Harmonic Motion

8.1.4Resonance

8.1.5End of Topic Test - Simple Harmonic Motion

8.1.6A-A* (AO3/4) - Simple Harmonic Motion

8.1.7End of Topic Test - Gravitational Fields

8.2Waves

8.2.1Progressive Waves

8.2.2Intensity of Waves

8.2.3Wave Speed & Phase Difference

8.2.4Longitudinal & Transverse Waves

8.2.5End of Topic Test - Progressive Waves

8.2.6Electromagnetic Waves

8.2.7Doppler Effect

8.2.8Sound Waves

8.2.9Measuring Sound Waves

8.2.10End of Topic Test - Waves

8.2.11Ultrasound Imaging

8.2.12Ultrasound Imaging 2

8.3Superposition

8.3.1Stationary Waves

8.3.2Stationary Waves 2

8.3.3End of Topic Test - Stationary Waves

8.3.4A-A* (AO3/4) - Stationary Waves

8.3.5Interference

8.3.6Interference 2

8.3.7End of Topic Test - Interference

8.3.8Diffraction

8.3.9Diffraction Gratings

8.3.10End of Topic Test - Diffraction

9Communication

9.1Communication Channels

9.1.1Communication Channels

9.1.2Modulation

9.1.3Attenuation

9.2Digital Communication

9.2.1Digital & Analogue Signals

9.2.2Representing Sound

10Electric Fields

10.1Electric Fields

10.1.1Coulomb's Law

10.1.2Electric Field Strength

10.1.3Electric Field Strength 2

10.1.4Electric Potential

10.1.5End of Topic Test - Electric Fields

10.1.6A-A* (AO3/4) - Electric and Gravitational Field

10.2Capacitance

10.2.1Capacitance

10.2.2Parallel Plate Capacitor

10.2.3Energy Stored by a Capacitor

10.2.4Capacitor Discharge

10.2.5Capacitor Charge

11Current Electricity

11.1Current Electricity

11.1.1Basics of Electricity

11.1.2Mean Drift Velocity

11.1.3Current-Voltage Characteristics

11.1.4End of Topic Test - Basics of Electricity

11.1.5Resistivity

11.1.6End of Topic Test - Resistivity & Superconductors

11.1.7Power and Conservation

11.1.8Microphones

11.1.9Components

11.1.10Relays

11.1.11Strain Gauges

11.2DC Circuits

11.2.1Circuits

11.2.2Potential Divider

11.2.3Emf & Internal Resistance

11.2.4End of Topic Test - Power & Potential

12Magnetic Fields

12.1Magnetic Fields

12.1.1Magnetic Flux Density

12.1.2End of Topic Test - Capacitance & Flux Density

12.1.3Moving Charges in a Magnetic Field

12.1.4Magnetic Flux & Flux Linkage

12.1.5Electromagnetic Induction

12.1.6Electromagnetic Induction 2

12.1.7Magnetic Flux Density

12.1.8Magnetic Resonance Scanning

12.2Alternating Currents

12.2.1Alternating Currents

12.2.2Operation of a Transformer

12.2.3End of Topic Test - Electromagnetic Induction & AC

12.2.4Rectification

13Modern Physics

13.1Quantum Physics

13.1.1The Photoelectric Effect

13.1.2The Photoelectric Effect Explanation

13.1.3End of Topic Test - The Photoelectric Effect

13.1.4Collisions of Electrons with Atoms

13.1.5Energy Levels & Photon Emission

13.1.6Wave-Particle Duality

13.1.7End of Topic Test - Absorption & Emission

13.1.8Band Theory

13.1.9Diagnostic X-Rays

13.1.10X-Ray Image Processing

13.1.11Absorption of X-Rays

13.1.12CT Scanners

13.2Nuclear Physics

13.2.1Rutherford Scattering

13.2.2Atomic Model

13.2.3Isotopes

13.2.4Stable & Unstable Nuclei

13.2.5A-A* (AO3/4) - Stable & Unstable Nuclei

13.2.6Alpha & Beta Radiation

13.2.7Gamma Radiation

13.2.8Particles, Antiparticles & Photons

13.2.9Quarks & Antiquarks

13.2.10Particle Interactions

13.2.11Radioactive Decay

13.2.12Half Life

13.2.13End of Topic Test - Radioactivity

13.2.14Nuclear Instability

13.2.15Mass & Energy

13.2.16Binding Energy

13.2.17A-A* (AO3/4) - Nuclear Fusion

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