What is the voltmeter?

The voltmeter is a device that is used to measure the electromotive force (e.m.f.) or the potential difference across a circuit component.

Fig 1 below shows a voltmeter that is connected to a dry cell.

Fig 1

The voltmeter is always connected in parallel to the power supply. That is the positive terminal of the power supply is connected to the positive terminal of the voltmeter. The negative terminal of the power supply is likewise connected to the negative terminal of the voltmeter.

Please note that by convention the positive terminal is red while the negative terminal is black.

Fig 2  is the same circuit but this time using symbols.

Fig 2

Should there be another circuit element like a bulb the voltmeter is connected in parallel to the bulb, if you want to measure the potential difference across the bulb,  of across the power supply if you want to measure the potential difference across the power supply while it is supplying current to the bulb.Again with the positive terminal of the power supply connected to the positive terminal of the voltmeter and the negative terminal of the power supply connected to the negative terminal of the voltmeter. Fig 3 below illustrates the two concepts.

Fig 3

In addition to the voltmeter in Fig 1 there are also voltmeters that are dual range.  That is they can measure voltages over two different ranges. A typical high school voltmeter has the 0 – 5 V and 0 – 15 V ranges. An examples can be seen in fig 4 below.

Fig 4

The way to use the voltmeter is to connect the negative terminal of the voltmeter to the negative terminal of the power supply and positive terminal of the power supply to either the 5 V positive terminal and the 15 V positive terminal depending on which range to be used. Fig 5 shows the voltmeter being used over the 0 – 5 V range while fig 6 shows the voltmeter being used over the 0 –15 V range.

Fig 5

Fig 6

Temperature and its measurement

under construction

Errors and uncertainties

 

Rules to perform mathematical operations

 Addition and subtraction/Addition and subtraction

Multiplication and division/Multiplication and division

lg and ln

Uncertainty and errors

Addition and subtraction

Multiplication and division

root, powers, etc

Errors

What is an error?

What is a zero error?

What is a parallax error?

Measurement, errors and uncertainties

Calculation

Calculation in Physics

Performing addition and subtraction

Performing multiplication and division

Performing Calculation with lg and ln

Uncertainties and errors

Uncertainty and How to process it

How to determine uncertainty in a derived quantity when addition or subtraction is performed?

How to determine uncertainty in derived quantity when multiplication or division is performed.

How to determine uncertainty in a derived quantity when powers, root,etc are involved.

Derived units

As we have seen in the last post there are 7 fundamental base units. From these 7 fundamental base units all the other units can be derived.

In fact if a quantity is not a basic quantity then it must certainly be a derived quantity and its unit a derived unit. The derived unit is based on one or more of the 8 fundamental base units. You must keep in mind that some quantities have units of their own based on famous scientists such as Joule (J) for energy or Newton (N) for force. For such quantities the unit can be used or the derived unit can be used.

We are now going to see several derived quantities and their derived units and how these derived units are obtained.

We are now going to see how these derived units are obtained. Once you know how to determine the derived units of common quantities like volume, force, etc then later on you will be able to determine the derived quantity for any other quantity.

So what is the method to obtain the derived unit of a quantity?

Example 1

We are going to start with a simple one: the derived unit for volume.

In order to deduce the derived unit of a quantity you need a formula to calculate the quantity. The formula must contain that you know the units in term of based unit.

Volume = length * width * height

Unit of [volume] = unit of [length * width * height]
= unit of [length] * unit of [width] * unit of [height]
= m * m *m
= m³

Example 2

What is the derived unit for acceleration?

In order to deduce the derived unit for acceleration, you must know a formula to calculate acceleration such as

Acceleration = velocity / time

The formula must contain quantities that you know the units in term of base units.

If in the new formula, there is quantity that you do not know the derived unit then you will also have to know the formula to calculate that quantity.

Velocity = displacement / time

You can now rewrite the formula for acceleration to

Acceleration = velocity / time
= (displacement / time) /time

So

the unit of acceleration = unit of [velocity / time]
= unit of [(displacement / time) /time]
= unit of [(displacement / time)] / unit of time
= (m/s) /s
= m *s^-1 * s^-1
= m s^-2

Was it easy?

Now let us have a look at another example to confirm your newly learned skills.

Example 3

What is the derived unit for pressure?

Have you worked it out?

Now you would remember that in order to find the derived unit you need to know a formula for the quantity in term of quantities that you already know the units.

Pressure = Force / surface are

Hence unit of pressure = unit of [force] / unit of [surface area]
= unit of [mass * acceleration] / unit of surface area]
= (kg * m/ s²)/m²
= (kg m * s^-2 * m ^-2
= Kg m^-1 s^-2


Do the following questions and post the answers in the comment section. I will give the correct answers later on after a few of you have submitted your answers.

Find the derived units for the following quantities.

1. Work done
2. Kinetic energy
3. Volume
4. Density

As you progress through the course you will meet more quantities that you would be able to derive the units.

Good luck and see you next time.

Base units

Units are the third aspect that is important when measuring in Physics. It can be the mistake that will ruin the whole measurement process.

Let us recap.

1. You need to identify the quantity that is to be measured eg length of the book.
2. you need to use the correct instrument to measure the quantity. In this case the 30 cm ruler.
3. Lastly you need to measure the length and write it with appropriate unit.

Imagine that you write the length of a 20 cm long book as 20 inches. Then it ruins the whole measurement process.

SI units

To avoid such mistakes scientist around the world have decided to use what is called the SI system of units. It is a standard that is used by all scientists such that when a particular quantity is being measures everyone uses the same units although the Americans and the British continue to use the old systems. This has resulted in costly mistakes and loss of human lives in the space industry.

Base units

The SI system is based on fundamental base units on which all other units can be derived.

The 7 fundamental base units are given in the table below.

Basic Quantity	Base unit	Symbol of base unit
Length	Metre	m
Time	Second	s
Mass	Kilogram	kg
Thermodynamic temperature	Kelvin	K
Luminous intensity	Candela	Cd
Electric current	Ampere	A
Amount of matter	Mole	Mol

These units are the 7 fundamental base units that are used in the SI system of units. Hence even though the quantities in the above table can be measured using other units, it is recommended that only these units are used.

The next part this series on derived units can be found here.

See you later my students.

How to perform calculation involving lg and ln in physics?

The physics students are often faced with calculations involving logarithm either to base 10 or the natural logarithm. Just like addition, subtraction, multiplication and division, the answer to a calculation involving either lg or ln has to be given in a certain form.

Let us have a look at an example and then later on we are going to see the law.

lg 12.3 = 1.0899

Now is 1.0899 the correct answer?

Let us see how the answer should have been written and after that we will discuss the reasoning behind.

lg 12.3 = 1.0899 = 1.090

Can you guess the reasoning behind? The number being used has 3 significant figures and as a result the answer is given to 3 decimal places.

Let us have a look at a second example.

ln 1.98 = 0.98503 = 0.985

Since the number used has three significant figures then the answer is given to three decimal places.

Did you get it?

The rule when calculating with lg and ln is simply

The answer to a calculation involving lg and ln is given to a certain number of decimal places equal to the number of significant figures of the number used.



Now some questions for you.

1. lg 0.67


2. ln 6.7


3. lg 122


4. ln 6.777

Here you go my students. I will give you the answers to these questions later on.

Good luck.

How to perform calculations in physics?

The young physicist is faced with a lot of calculations during his studies. Sadly however very few of you are able to perform the properly and this will be a problem for you both in theoretical and practical classes. In this five part series we are going to teach our young physicists, you, how to perform calculations the way it should be and how to give the answer in the appropriate form.

I have divided this series into the following parts;

1. Addition and subtraction

2. Multiplication and division

3. Lg and ln

5. Other mathematical operations (under construction)

At the end of this series, you would be well equipped for the physics course so sit tight and hop in. Remember if you have any questions leave them at the end of the blog in the comment section.

How to perform mutiplication and division?

Division and multiplication is often encountered in physics and it is very important that you know how to give the answer in the appropriate form.

Let us have a look at how division and multiplication is performed.

Multiplication

Let us see an example of a multiplication and see how to give the answer in the appropriate form.

23.2 * 3.1 = 71.92 = 72

Can you guess why the answer is 72?

Firstly you have to look at the number of significant figures in the two number used.

23.2    3 significant figures

3.1      2 significant figures

One of the numbers (3.1) has the smallest number of significant figures (2) as a result the answer must be given to 2 significant figures. Hence the answer is given as 72.

Let us have a look at a second example.

22.34 * 123 = 2747.82 = 2750

123 has 3 significant figures and 22.34 has 4 significant figures so the answer is given to 3 significant figures.

Have you guessed the law yet? If yes write it down. If not keep thinking. We will see it at the end of the post.

Division

In a way division is somewhat related to multiplication. Let us have a look at an example and see how the answer is given.

14.2 / 2.333 = 6.08658 = 6.09

As you can see it is similar to multiplication. The two number used has 3 and 4 significant figures respectively. And as a result the answer is given to 3 significant figures.

Let us have a look at a second example.

1.33 / 3.0 = 0.44333

Can you guess how to write the answer in the correct form?

Yes you have guessed right. It is 0.44. Since the two numbers used are at 3 and 2 significant figures respectively, then the answer is given to 2 significant figures.

So have you guessed the rule that govern the multiplication and division? Here it is!!

When a multiplication or a division is performed, the answer is given to the same number of significant figures as the number used with the smallest number of significant figures.



It is now time to do some exercises.

1. 1.2 * 343


2. 2.3 / 3.55


3. 3.4 * 0.2222


4. 3.555 * 434 / 0.32

I will give the correct answer after a few of you have submitted your answers in the comment section.

See you later my students.

How to perform addition and subtraction in physics

In physics we often encounter calculations where you have to add two numbers together or we had to subtract one number from another. This is particularly important when data from practical sessions are processed even though additions and subtractions are often met in the syllabus.

However, as I have said in the introduction, the answer must be given to a certain number of decimal place. If you cannot say what the number of decimal place a number has, please refer to this post on decimal place.



Addition

Now let us see an example on how to add two numbers.

4.43

7.6    +

_____

12.03

____

12.0     Final answer.

So how do you give the answer to the appropriate number of decimal places? Add the two numbers and you get the answer 12.03. But this is not the final answer to the addition.

Before you write the final answer, look at the two numbers and determine the number of decimal places for each.

4.43    2 decimal places

7.6      1 decimal place

Now what is the smallest number of decimal places in the two numbers?

7.6 has 1 decimal place so the answer must have 1 decimal place. So the final answer is 12.0 with 1 decimal place.

Let us have a look at a second example.

67.54             2 decimal places

45.345            3 decimal places

______

112.885

112.89            Final answer2  decimal places

This is not the final answer. The two numbers used has 2 and 3 decimal places. So the final answer must be given to 2 decimal places. So the final answer is 112.89

Easy isn’t it.



Subtraction

Now we are going to see how subtraction is done. Here an example.

34.9

32.09  -

____

2.81

2.8      Final answer

So have you guessed how the answer is obtained?

The first number has 1 decimal place and the second number has 2 decimal places. As a result the answer must have 1 decimal place.

Let us have a look at a second example.

123.7             1 decimal place

3.433         3 decimal places

______

120.267

120.3             Final answer

1 decimal place

Have you got it? Let me summarise this with a rule.

When an addition or a subtraction is performed the answer is given to the same number of decimal places as the number used that has the smallest number of decimal places.

It is very important that you remember this law.

It is now time to do some exercises.

1. 12.45 + 34.555


2. 2.3 + 23.4445


3. 3.444 - 545


4. 34.3 – 34.111


5. 44.009 – 23.2

Do the following exercises and leave the answer in the comment section. I will give the correct answer later on when a few of you have submitted your answers.

What is a physical quantity?

Physical quantities

A physical quantity is a property of an object that can be measured with a measuring instrument.For example length, width, time, weight, etc.

It is important for you to be able to say which instrument is used to measure which physical quantity.The table below shows a few examples of physical quantities and the instruments used to measure them.

Physical quantity Instrument

Length                                                        Metre rule

Temperature                                            Thermometer

Time                                                             Stopwatch

Volume                                                       Measuring cylinder

Of course as we go through the different chapters we will be able to introduce more physical quantities and their measuring instruments.

Basic and derived quantities

Quantities can be divided into two types :

1. Base quantities

2. Derived quantities

Basic quantities

Basic quantities are the fundamental quantities that are not related to each other and that are use to derive all other quantities.

There are seven basic quantities. They are

1.  length

2.  time

3. mass

4. Thermodynamic temperature

5. electric current

6. amount of substance

7. luminous intensity

Derived quantities

Derived quantities are just quantities that are derived from one or more basic quantities.

For example area is a derived quantity because it is derived from the basic quantity length.

Area = length * length

Volume is a derived quantities because it is derived from the basic quantity length.

volume = length * length * length

density is a derived quantity because it is derived from length and mass, two basic quantities.

density = mass/(length * length * length)

As you can see all other quantities apart from the 7 basic quantities are derived from the seven basic quantities and it can easily be shown as in the example above.

Can you show what are the basic quantities that are used to derive the following derived quantities?

a) force

b)  kinetic energy

c) power

d) pressure

I would give the answer after a few of you would have give your answers.

Good luck and see you next time.

Physical quantities and units

Physical quantities

What is a physical quantities?

Subject of formula

Subject of formula: The basics

Vectors

What is a vector and how to add vector

Scalar and vector quantities

How to subtract one vector from another

Units

Base Units
Derived units

Homogeneity of equations 

Prefixes

Prefixes  and how to use them

Measurement of physical quantities

Volume and volume of irregular objects

Prefixes

How to use prefixes