11.2.5

Capacitor Charge

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Charging a Capacitor

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

Voltage

Voltage

  • The formula for this graph is:
    • V=V0(1−e−tRC)V=V_0(1-e^{-\frac{t}{RC}})
  • Where V0V_0 is the final potential difference across the capacitor.
Charge

Charge

  • The formula for this graph is:
    • Q=Q0(1−e−tRC)Q=Q_0(1-e^{-\frac{t}{RC}})
  • Where Q0Q_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

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

Set up

  • A circuit should be set up as in the diagram.
Method - charging

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

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

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

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

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.
Jump to other topics
1

Physical Quantities & Units

1.1

Physical Quantities & Units

1.1.1Use of SI Units1.1.2SI Prefixes, Standard Form & Converting Units1.1.3End of Topic Test - Units & Prefixes1.1.4Avogadro's Constant1.1.5Scalars & Vectors
1.2

Errors & Uncertainty

1.2.1Measuring Length, Time & Volume1.2.2Measuring Temperature1.2.3Circuit Measurements1.2.4Limitation of Physical Measurements1.2.5Uncertainty1.2.6Estimation1.2.7Displaying Data1.2.8End of Topic Test - Measurements & Errors
2

Kinematics

2.1

Equations of Motion

2.1.1Motion in a Straight Line2.1.2Graphs of Motion2.1.3Bouncing Ball Example2.1.4End of Topic Test - Motion in a Straight Line2.1.5Acceleration Due to Gravity
3

Dynamics

3.1

Momentum & Newton's Laws of Motion

3.1.1Mass & Inertia3.1.2Newton's Laws3.1.3Momentum3.1.4End of Topic Test - Newton's Laws & Momentum3.1.5A-A* (AO3/4) - Newton's Third Law
3.2

Non-Uniform Motion

3.2.1Projectile Motion
3.3

Linear Momentum & Conservation

3.3.1Conservation of Momentum
4

Force, Density & Pressure

4.1

Force, Density & Pressure

4.1.1Fields4.1.2Force in Uniform Fields4.1.3Friction4.1.4Buoyancy4.1.5Terminal Speed4.1.6End of Topic Test - Acceleration Due to Gravity4.1.7Centre of Mass4.1.8Forces & Equilibrium4.1.9End of Topic Test - Scalars & Vectors4.1.10Moments4.1.11End of Topic Test - Moments & Centre of Mass4.1.12Density4.1.13Pressure
5

Work, Energy & Power

5.1

Work, Energy & Power

5.1.1Work & Energy5.1.2Power & Efficiency5.1.3Conservation of Energy5.1.4End of Topic Test - Work, Energy & Power
5.2

Gravitational Fields

5.2.1Newton's Law5.2.2Gravitational Field Strength5.2.3Gravitational Potential
6

Deformation of Solids

6.1

Materials

6.1.1Bulk Properties of Solids6.1.2Energy in Materials6.1.3Young Modulus6.1.4End of Topic Test - Materials
7

Waves

7.1

Simple Harmonic Motion

7.1.1Simple Harmonic Motion7.1.2Simple Harmonic Systems7.1.3Energy in Simple Harmonic Motion7.1.4Resonance7.1.5End of Topic Test - Simple Harmonic Motion7.1.6A-A* (AO3/4) - Simple Harmonic Motion7.1.7End of Topic Test - Gravitational Fields
7.2

Waves

7.2.1Progressive Waves7.2.2Intensity of Waves7.2.3Wave Speed & Phase Difference7.2.4Longitudinal & Transverse Waves7.2.5End of Topic Test - Progressive Waves7.2.6Electromagnetic Waves7.2.7Doppler Effect7.2.8Sound Waves7.2.9Measuring Sound Waves7.2.10End of Topic Test - Waves7.2.11Ultrasound Imaging7.2.12Ultrasound Imaging 2
8

Superposition

8.1

Superposition

8.1.1Stationary Waves8.1.2Stationary Waves 28.1.3End of Topic Test - Stationary Waves8.1.4A-A* (AO3/4) - Stationary Waves8.1.5Interference8.1.6Interference 28.1.7End of Topic Test - Interference8.1.8Diffraction8.1.9Diffraction Gratings8.1.10End of Topic Test - Diffraction
9

Thermal Physics

9.1

Circular Motion

9.1.1Circular Motion9.1.2Circular Motion 29.1.3End of Topic Test - Circular Motion
9.2

Thermal Physics

9.2.1Temperature9.2.2Measuring Temperature9.2.3Ideal Gas Law9.2.4Ideal Gases9.2.5Boyle's Law & Charles' Law9.2.6Molecular Kinetic Theory Model9.2.7Molecular Kinetic Theory Model 29.2.8Thermal Energy Transfer9.2.9Thermal Energy Transfer Experiments9.2.10End of Topic Test - Thermal Energy & Ideal Gases9.2.11First Law of Thermodynamics
10

Communication

10.1

Communication Channels

10.1.1Communication Channels10.1.2Modulation10.1.3Attenuation
10.2

Digital Communication

10.2.1Digital & Analogue Signals10.2.2Representing Sound
11

Electric Fields

11.1

Electric Fields

11.1.1Coulomb's Law11.1.2Electric Field Strength11.1.3Electric Field Strength 211.1.4Electric Potential11.1.5End of Topic Test - Electric Fields11.1.6A-A* (AO3/4) - Electric and Gravitational Field
11.2

Capacitance

11.2.1Capacitance11.2.2Parallel Plate Capacitor11.2.3Energy Stored by a Capacitor11.2.4Capacitor Discharge11.2.5Capacitor Charge
12

Current Electricity

12.1

Current Electricity

12.1.1Basics of Electricity12.1.2Mean Drift Velocity12.1.3Current-Voltage Characteristics12.1.4End of Topic Test - Basics of Electricity12.1.5Resistivity12.1.6End of Topic Test - Resistivity & Superconductors12.1.7Power and Conservation12.1.8Microphones12.1.9Components12.1.10Relays12.1.11Strain Gauges
12.2

DC Circuits

12.2.1Circuits12.2.2Potential Divider12.2.3Emf & Internal Resistance12.2.4End of Topic Test - Power & Potential
13

Magnetic Fields

13.1

Magnetic Fields

13.1.1Magnetic Flux Density13.1.2End of Topic Test - Capacitance & Flux Density13.1.3Moving Charges in a Magnetic Field13.1.4Magnetic Flux & Flux Linkage13.1.5Electromagnetic Induction13.1.6Electromagnetic Induction 213.1.7Magnetic Flux Density13.1.8Magnetic Resonance Scanning
13.2

Alternating Currents

13.2.1Alternating Currents13.2.2Operation of a Transformer13.2.3End of Topic Test - Electromagnetic Induction & AC13.2.4Rectification
14

Modern Physics

14.1

Quantum Physics

14.1.1The Photoelectric Effect14.1.2The Photoelectric Effect Explanation14.1.3End of Topic Test - The Photoelectric Effect14.1.4Collisions of Electrons with Atoms14.1.5Energy Levels & Photon Emission14.1.6Wave-Particle Duality14.1.7End of Topic Test - Absorption & Emission14.1.8Band Theory14.1.9Diagnostic X-Rays14.1.10X-Ray Image Processing14.1.11Absorption of X-Rays14.1.12CT Scanners
14.2

Nuclear Physics

14.2.1Rutherford Scattering14.2.2Atomic Model14.2.3Isotopes14.2.4Stable & Unstable Nuclei14.2.5A-A* (AO3/4) - Stable & Unstable Nuclei14.2.6Alpha & Beta Radiation14.2.7Gamma Radiation14.2.8Particles, Antiparticles & Photons14.2.9Quarks & Antiquarks14.2.10Particle Interactions14.2.11Radioactive Decay14.2.12Half Life14.2.13End of Topic Test - Radioactivity14.2.14Nuclear Instability14.2.15Mass & Energy14.2.16Binding Energy14.2.17A-A* (AO3/4) - Nuclear Fusion

Practice questions on Capacitor Charge

Can you answer these? Test yourself with free interactive practice on Seneca — used by over 10 million students.

  1. 1
    Graphs of voltage and charge against time when discharging a capacitor have:True / false
  2. 2
    When charging a capacitor, $$V_0$$ represents:Multiple choice
  3. 3
    Why is it important to charge a capacitor with the correct polarity?Multiple choice
  4. 4
    Charging a capacitorPut in order
  5. 5
    The time constant can be found by reading off the value of a voltage-time graph at what percentage of the initial voltage?Multiple choice
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Capacitor Discharge

Basics of Electricity