Bredhurst Receiving and Transmitting Society

Syllabus Sections:-

Power in DC circuits

3c.1 Understand and apply the formula relating power to potential difference, current and resistance.

The formulae are :- P = V x I, V = I x R, P = V² / R, P = I² x R

which can also be written using the mathematical notation of placing two letter together meaning multiply them together as:-

The formulae are :- P = VI, V = IR, P = V² / R, P = I²R

In the Foundation Licence course you were introduced to two magic triangles  one relating to power, potential difference and current P = V x I, and another one relating to potential difference, current and resistance V = I x R. The triangles were again used in the intermediate Licence course.

Now we are going to develop your knowledge further and see what can be done with the two formula and a little bit of mathematics which either you may have forgotten from school or may not even have learned yet.

If you look at the two formula you will note that there is some similarity in that both have V and I.

We can therefore mathematically substitute the V in P = V x I  by the V = I x R  and we would get :-

So from this P = V x I  

which with from V = I x R we substituted the V by the I x R and the result is  

P = I x R x I

I x I = I² in english that is I times I which equals I squared I²

thus P = I² x R

which was the last formula in the syllabus section so what about the other one?

well from V = I x R also we manipulate the formula to give V / R = I

With the I is substituted by V / R  in P = V x I

we get P = V x V / R

thus P = V² / R  which is the other equation mentioned in the syllabus.

So you do not have to actually have to learn

P = V² / R    &   P = I² x R

assuming that you can what is called derive them from the two basic formulae of

P = V x I   &   V = I x R

and at least now you know where they come from !!!