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A Mathematical Technique For Studying Dimensions Of Physical Quantities?

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The only 'technique' required is the ability to manipulate fractions.e.g.Voltage is defined as the work done per coulomb; Now   work = force x displacement = mass x acceleration x displacement; So voltage = (mass x acceleration x displacement ) / Charge. But, acceleration = displacement / (time)^2,   So voltage = (mass x displacement x displacement) / [(time)^2 x Charge]

There are only a few basic physical quantities from which many others can be derived.e.g mass, length/displacement, time, quantity of charge, luminous intensity etc..Having defined voltage above, consider this:-
Resistance = volts/amps= (mass x displacement x displacement)/[(time)^2 x Charge x amps]      But, amps = Charge / time,   thus
Resistance = (mass x displacement x displacement)/[(time)^2 x Charge x charge / time]                                             =(mass x displacement x displacement)/[time x Charge x Charge]And so on......

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