Hi all, I in my text they first did a phasor-diagram solution to a series LCR circuit and brought Z= under root of (R^2 +(Xc^2-XL^2)). After this they use a differential equation for series LCR circuit and actually did not solve such hard two degree differential equation, rather they assume the solution to be q= q• sin(wt+€) and taking its first and second derivatives and used them in orignal differential equation. Then they divide it by Z= square root of(R^2+ (Xc^2-XL^2)) and tan¥=R/Z so that finally they get q• wZcos(wt+€-¥)= v• sinwt, from this equation they concluded that v•= q•wZ! This is where I am confused, how can one conclude this according to maths rule. If A*B= C*D, how can we say A=B? This is where I find it odd. And yes I know the maximum values of the quanties on the sides must be equal as the maximum values of both sin and cos are one(1) but these the two(sin and cos) may not keep their maximum value at same time and hence to take both as one(1) at a single time is to distort this very fact that they may have different values also. Thanks a bunch!!!