Page:Calculus Made Easy.pdf/261

 The result, when cleared down, is:

Inserting this value in [A], we get

To simplify still further, let us imagine an angle $$\phi$$ such that $$\tan \phi = \dfrac{2 \pi n b}{ a}$$. Then

and

Substituting these, we get:

which may be written

which is the solution desired.

This is indeed none other than the equation of an alternating electric current, where $$g$$ represents the amplitude of the electromotive force, $$n$$ the frequency, a the resistance, $$b$$ the coefficient of self-induction of the circuit, and $$\phi$$ is an angle of lag.