# How can you divide the 'Volt' by 'Ampere' and get 'Ohms'

#### Sauve

Joined Nov 16, 2007
4
Dear Members,

I have just begun to learn electronics and I have run into a confusion already.

How V, Volt can be divided by A, Ampere and then a third unit O, Ohm obtained. Shouldnt the Units be same?

From the background in maths I have, which isn't very high, I knew that only similar UNITS are valid for division, multiplication, etc.

I think we were required to convert to similar units and then do operations.

Can anyone you please help me find what I am missing. I am open to learning and have also started looking at K. A. Stroud's Engineering Maths.

Thanks,
Dutta.

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#### chesart1

Joined Jan 23, 2006
269
Dear Members,

I have just begun to learn electronics and I have run into a confusion already.

How V, Volt can be divided by A, Ampere and then a third unit O, Ohm obtained. Shouldnt the Units be same?

From the background in maths I have, which isn't very high, I knew that only similar UNITS are valid for division, multiplication, etc.

I think we were required to convert to similar units and then do operations.

Can anyone you please help me find what I am missing. I am open to learning and have also started looking at K. A. Stroud's Engineering Maths.

Thanks,
Dutta.
Actually it is defined in the same units. Instead of using the original units, the term ohm is used. An ohm is defined as the electrical resistance in a circuit where one volt produces one amp of current. One ohm equals one volt per ampere.

#### recca02

Joined Apr 2, 2007
1,212
similar UNITS are valid for division, multiplication, etc.
actually different units can be multiplied or divided.
like f=mass*acceleration.
but addition or subtraction or use of equal(=) sign is possible only with similar units.

f=ma, ma must have same units as f,
f-ma=X ;ma , X must have same units as f;
f+ma=X
here f, ma and X must have same units.

The rest of ur query was better answered by Mr chesart .

#### GS3

Joined Sep 21, 2007
408
Just like a Nautical Mile per hour is a Knot. Would you rather say "Knots" or "Nautical Miles per Hour"?

Would you rather say "Volts per Ampere" or "Ohms"?

#### Dave

Joined Nov 17, 2003
6,969
The derivation of volts and ohms will help:

The volt is defined as the potential difference across a conductor when a current of one ampere dissipates one watt of power:

V = W/A

Which can be shown to be one Joule of energy per coulomb:

V = J/C

By definition:

J = N.m (newtons x Metres)

C = A.s (Amps x Seconds)

Therefore:

V = (N.m)/(A.s)

Substituting units, volts is derived as:

V = (kg.m^2)/(A.s^3) (see. http://en.wikipedia.org/wiki/Volt#Definition)

Divide that by the unit of current, i.e. Amps:

R = V/I = (kg.m^2)/(A^2.s^3) - this is the unit of resistance, or Ohms

This correlates to the definition of Ohms as the unit of resistance: An ohm is the electrical resistance offered by a current-carrying element that produces a voltage drop of one volt when a current of one ampere is flowing through it (see. http://en.wikipedia.org/wiki/Ohm#Definition)

Dave

#### studiot

Joined Nov 9, 2007
4,998
Some rules to help

A number eg 5 has no units
A quantity eg 5 metres has both a number and units

You can add (subtract) a quantity from another in the same units 5metres-3metres=2metres
The result is always in the same units as you started.
But 3metres-5 metres= -2metres may or may not make sense, depending upon the context.

You cannot add (subtract) a quantity from another in the different units 5metres-3grammes is nonsense.

You cannot add (subtract) a quantity and a number 5metres+5 makes no sense.

Multiplication

You can multiply (divide) a quantity by a number 5 times 1 metre = 5 metres
The result is always in the same units as you started.

You can multiply a quantity by another quantity in the same units.
The result is always in the different units from those you started with. eg 5metres times 5 metres=25 square metres
Sometimes the the result is important enough to be called a new quantity eg 5metres measures length; 25 square metres measures area.

You can multiply a quantity by another quantity in the different units.
The result is always in the different units from those you started with. eg 5metres times 25 square metres=125 cubic metres
Sometimes the the result is important enough to be called a new quantity eg 5metres measures length; 25 square metres measures area; 125 cubic metres measures volume.

You can divide a quantity by another quantity in the same units.
The result is always a number. eg 25metres divided by 5 metres=5
This result tells you that the first length is 5 times as long as the second.

You can divide a quantity by another quantity in the different units.
The result is always in different units from those you started with. eg 5volts divided by 1 amp=5 volts per amp
Sometimes the the result is important enough to be called a new quantity eg 5 volts per amp is called 5 ohms.

You cannot divide by zero in any system

When you study 'Stroud' you will find that there can be more complicated rules for the actual processes of addition, subtraction, multiplication and division of quantities. Look in the section on Vectors.

#### Sauve

Joined Nov 16, 2007
4
Thanks for the responses.

Each response adds value and had helped me understand the Law (not the division issue) I was groping with. I think OHM's law, is not simply a case of arithmetic division, it's the mathematical representation of a fact.

Probably there are more to some Laws, than division (or Multiplication).

I will go through the Math's Book immediately, then tackle Electronics.
To save time the other choice, I have is to jump to electronics and create projects accepting things as they are...not questioning too much...they are time-tested.

But this conversation with you all was very very useful.

Thanks again,
Dutta.

#### Dave

Joined Nov 17, 2003
6,969
I will go through the Math's Book immediately, then tackle Electronics.
To save time the other choice, I have is to jump to electronics and create projects accepting things as they are...not questioning too much...they are time-tested.
Indeed doing some basic experiments may encourage some of your understanding of the basics, after which it may be advisable to revisit some of the theory look at it from a different perspective.

Can I suggest you look at some of the simple experiments from Volume VI of the e-book: http://www.allaboutcircuits.com/vol_6/index.html

Taking a leap of faith at this stage may pay off when you return to the theory at a later stage. You can then return to this thread and ask further questions. We wish you well.

Dave