Mega M 1 000 000 kilo k 1000 milli m 1/(1000) micro u 1/(1 000 000) nano n 1/(1 000 000 000) pico p 1/(1 000 000 000 000)


Throughout this book equations have been printed in as many forms as are normally needed so that the reader should not have to transpose the equations. For example, Ohm’s law is given in all three familiar forms of V=IR,R=V/I and I=V/R.The units that must be used with such formulae are shown and must be adhered to – if no units are quoted then fundamental units (amp, ohm, volt) are implied.For example,the equation X=1/(2pfC)is used to find the reactance of acapacitor in ohms, using C in farads and f in hertz. If the equation is to be used with values given in uF and kHz then values of 0.1mF and 15 kHz are entered as 0.1×10−6and 15×103.Alternatively, the equation can be written as X=1/(2pfC) MW using values off in kHz and C in nF.In all equation multiplication is normally indicated by the use of a dot, such as f.C or by close printing as shown above in 2 * pi *f *C. Where brackets are used in an equation, the quantities within the brackets should be worked out first, and where there are brackets within brackets, the portion of the

equation in the innermost brackets must be worked out first, followed by the material in the outer brackets. Apart from brackets, the normal order of working out is to carry out multiplication and divisions first followed by additions and subtractions. For example
2 (3+5) is 2×8=16 and 2 + (3×5) is 2+15 =17 Transposing, or changing the subject of an equation, is simple provided that the essential rule is remembered: an equation is not altered by carrying out identical operations on each side Example: Y=(5a X + b) / C is an equation that can be transposed so that it can be used to find the value of X when the other quantities are known.The procedure is to keep changing both sides so that X is left isolated.Starting with Y=5aX+bC the steps are as follows: (a) Multiply both sides by C, the result is CY=5aX+b (b) Subtract b from both sides, the result is CY−b=5aX (c) Divide both sides by 5a, the result is ( CY−b )/ 5a =X So that the equation has become X=CY−b5awhich is the transposition we required 