To calculate the Time Constant we use T = RC
To calculate the Time Constant we use T = RC
Example of circuit used for testing capacitor charge and discharge.
Example of circuit used for testing capacitor charge and discharge.

Capacitors discharge exponentially, the rate of discharge is known as the time constant
Capacitors discharge exponentially, the rate of discharge is known as the time constant

We can also use similar equations to calculate the Voltage or Current at any point
We can also use similar equations to calculate the Voltage or Current at any point
When the equation is compared with y =mx+c m = 1/RC & C = ln Io
When the equation is compared with y =mx+c m = 1/RC & C = ln Io
To calculate the charge left on a capacitor at any point we use this equation.
To calculate the charge left on a capacitor at any point we use this equation.
Capacitor Discharge
Capacitor Discharge
When the switch is at A the capacitor charges exponentially up to a point where the capacitor cannot hold anymore electrons

When the switch is at A the capacitor charges exponentially up to a point where the capacitor cannot hold anymore electrons

When 2 Pendulums are suspended from the same piece of string when one pendulum is displaced it can transfer energy to the other pendulum causing it to swing
When 2 Pendulums are suspended from the same piece of string when one pendulum is displaced it can transfer energy to the other pendulum causing it to swing
This occurs because the pendulums have the same length string and as the resonant frequency of the pendulums depends on the length of the string they have the same resonant frequency.
This occurs because the pendulums have the same length string and as the resonant frequency of the pendulums depends on the length of the string they have the same resonant frequency.

Thus when the first pendulum is displaced it tugs on the main string which in turn tugs on the second pendulum causing it to begin oscillating.
Thus when the first pendulum is displaced it tugs on the main string which in turn tugs on the second pendulum causing it to begin oscillating.

Coupled Pendula
Coupled Pendula

This process continues with each pendulum speeding up and slowing down until all the energy is expended.
This process continues with each pendulum speeding up and slowing down until all the energy is expended.

When the first pendulum oscillates at its MAX displacement the second pendulum oscillates at mid displacement. The transfer of energy causes the first pendulum to slow down and halt oscillating.
When the first pendulum oscillates at its MAX displacement the second pendulum oscillates at mid displacement. The transfer of energy causes the first pendulum to slow down and halt oscillating.

Data Logging is often used where many measurements need to be taken in a short space of time or over a long period of time
Data Logging is often used where many measurements need to be taken in a short space of time or over a long period of time

Data Logging can be automated so can be used in remote or hostile environments where human interaction may not be possible i.e. Polar Regions, Space etc.
Data Logging can be automated so can be used in remote or hostile environments where human interaction may not be possible i.e. Polar Regions, Space etc.

Data Logging is a process by which measurements are taken using sensors connected to a computer
Data Logging is a process by which measurements are taken using sensors connected to a computer

Data Logging
Data Logging

Data Logging is very useful as it can automatically sort data into tables and graphs thus making analysing the data a quicker process.
Data Logging is very useful as it can automatically sort data into tables and graphs thus making analysing the data a quicker process.

Cons of data logging: Equipment can be very expensive, Sensors must be calibrated or results will be inaccurate.
Cons of data logging: Equipment can be very expensive, Sensors must be calibrated or results will be inaccurate.

Above is an example of a data logger setup with the sensor connected to an interface box which allows the computer to read the data and sort it.
Above is an example of a data logger setup with the sensor connected to an interface box which allows the computer to read the data and sort it.

This ionising property is what is used to differentiate them between other forms of radiation such as Infra-red and radio.
This ionising property is what is used to differentiate them between other forms of radiation such as Infra-red and radio.

Gamma & beta radiation are both ionising radiation which means they have the ability to pull electrons from neutral atoms creating Ions.
Gamma & beta radiation are both ionising radiation which means they have the ability to pull electrons from neutral atoms creating Ions.
The most common way of detecting ionising radiation is to use a gas filled tube called a Geiger Muller Tube.
The most common way of detecting ionising radiation is to use a gas filled tube called a Geiger Muller Tube.

Absorption of gamma/beta radiation
Absorption of gamma/beta radiation

Beta radiation is stopped by thin sheets of aluminium however gamma requires a few cms of lead to be stopped.
Beta radiation is stopped by thin sheets of aluminium however gamma requires a few cms of lead to be stopped.

Data loggers are often used to measure the count rate produced by the radioactive sources.
Data loggers are often used to measure the count rate produced by the radioactive sources.

The way this device works relies on the ionising properties of the radiation, when beta or gamma radiation enters the tube it ionises the gas allowing it to briefly conduct.
The way this device works relies on the ionising properties of the radiation, when beta or gamma radiation enters the tube it ionises the gas allowing it to briefly conduct.

During that short period the voltage produced is amplified and counted as one ionisation.
During that short period the voltage produced is amplified and counted as one ionisation.

Random errors are errors that are beyond human control such as electrical noise affecting an ammeter reading
Random errors are errors that are beyond human control such as electrical noise affecting an ammeter reading

Systematic error are errors that are brought by the equipment or its operator such as a calliper not reading zero when it should be.
Systematic error are errors that are brought by the equipment or its operator such as a calliper not reading zero when it should be.

Accuracy relates to how close the reading is to the true value and is improved by reducing systematic errors.
Accuracy relates to how close the reading is to the true value and is improved by reducing systematic errors.
There are 2 types of error when taking measurements; Random & systematic
There are 2 types of error when taking measurements; Random & systematic

Uncertainty
Uncertainty

Precision relates to how close the repeated readings are to each other and is improved by reducing random errors.
Precision relates to how close the repeated readings are to each other and is improved by reducing random errors.

The uncertainty caused by random errors can be calculated by taking the mean of the repeated reading then calculating the difference between the mean and the smallest value
The uncertainty caused by random errors can be calculated by taking the mean of the repeated reading then calculating the difference between the mean and the smallest value

The uncertainty caused by systematic errors is the smallest division of the instrument you are using i.e. 30cm ruler uncertainty is +/- 1mm
The uncertainty caused by systematic errors is the smallest division of the instrument you are using i.e. 30cm ruler uncertainty is +/- 1mm

When combining values which have an uncertainty, the uncertainty must also be combined. E.g. 40 +/- 3 + 20 +/- 2 = 60 +/- 5
When combining values which have an uncertainty, the uncertainty must also be combined. E.g. 40 +/- 3 + 20 +/- 2 = 60 +/- 5

We can calculate the percentage uncertainty by dividing the absolute uncertainty by the obtained values and then multiplying by 100 to get a percentage
We can calculate the percentage uncertainty by dividing the absolute uncertainty by the obtained values and then multiplying by 100 to get a percentage

This rule stays the same even when the values are being multiplied or divided
This rule stays the same even when the values are being multiplied or divided

Task – Taking Individual Results | Done? | Apparatus setup | | Values have appropriate units | | Values have appropriate significant figures | | Repeats taken | | Mean of repeats calculated | | Task – Graph | Done? | Axis labelled with units | | Axis go up in incremental values | | Lines drawn with a ruler | | Gradient Calculated and clearly shown | | Have used a sharp pencil to mark on points | | Graph is titled | |

Task Table of results | Done? | Table has headings with units | | Table is drawn with straight lines | | Repeats are tabulated | | Appropriate Significant figures used | | Correct units used | | | |

Task Finding the gradient | Done? | Lines to show where values have been obtained | | Values clearly labelled | | Appropriate units used | | | | | |

The time taken for an oscillating object to complete one full oscillation is called the time period, T. It is measured in seconds. If a number of oscillations are involved we can work out the time period by dividing the total time taken by the number of oscillations completed:

The time taken for an oscillating object to complete one full oscillation is called the time period, T. It is measured in seconds. If a number of oscillations are involved we can work out the time period by dividing the total time taken by the number of oscillations completed:

We can also use the following equations to calculate MAX speed and MAX displacement
We can also use the following equations to calculate MAX speed and MAX displacement
We can use the following equations to calculate displacement, velocity & acceleration where x is displacement, f is the frequency, t is the time of the oscillation & A is the amplitude. a is acceleration
We can use the following equations to calculate displacement, velocity & acceleration where x is displacement, f is the frequency, t is the time of the oscillation & A is the amplitude. a is acceleration
Used for a pendulum system
Used for a pendulum system
Used for a mass spring system
Used for a mass spring system
We can use the equations below for working out the time period of 2 different oscillating systems
We can use the equations below for working out the time period of 2 different oscillating systems
SHM is an oscillation in which the acceleration is directly proportional to the displacement from the mid-point, and is directed towards the mid-point.
SHM is an oscillation in which the acceleration is directly proportional to the displacement from the mid-point, and is directed towards the mid-point.
SHM Oscillations
SHM Oscillations
At MAX displacement the bob has 0 Velocity yet MAX acceleration.
At MAX displacement the bob has 0 Velocity yet MAX acceleration.
At the equilibrium position the bob has 0 displacement & 0 Acceleration as it is at MAX velocity so there is no resultant force
At the equilibrium position the bob has 0 displacement & 0 Acceleration as it is at MAX velocity so there is no resultant force