Similarities in physics

We note the similarities between the equations for the mechanical and electrical cases

......(1)

and

...........(2)

where we have written dx/dt for the velocity v and dq/dt for the current I, in order to bring out more sharply the similarity of the two cases. In both cases we have the identical forms

......(3)

where α and β are constants and Z = Z(t) is the oscillating quantity. In the mechanical case Z stands for the displacement x, and in the electrical case for the charge q. Thus all we have learned about mechanical oscillators can be carried over to electrical oscillators. Moreover we can see a direct correspondence between the two sets of physical quantities involved:

• q takes the place of x;
• L takes the place of m;
• 1/C takes the place of k.
For example, the inductance L is the electrical analogue of mechanical inertia m. These analogies enable us to build an electrical circuit that exactly mimics the operation of a mechanical system. This is useful because in the development of a mechanical system it is much easier to change, for example, the value of a capacitor in the analogue circuit than to manufacture a new mechanical component.