The voltage of an ac supply varies with time (t) asV = 120 sin 100 t cos 100 t. The maximumvoltage and frequency are :
Question
The voltage of an ac supply varies with time (t) asV = 120 sin 100 t cos 100 t. The maximumvoltage and frequency are :
Solution
The given equation is in the form of a product of sine and cosine functions. It can be rewritten using the double angle identity sin(2A) = 2sin(A)cos(A).
So, V = 120 sin 100πt cos 100πt can be rewritten as V = 60 sin (2*100πt).
The maximum voltage (Vmax) is the amplitude of the sinusoidal function, which is 60 volts.
The frequency (f) of the function can be found from the coefficient of t in the argument of the sine function. The general form of the function is V = Vmax sin(2πft), so 2*100π = 2πf. Solving for f gives f = 100 Hz.
So, the maximum voltage is 60 volts and the frequency is 100 Hz.
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