The electricity in your house is alternating current because the current varies sinusoidally with time. The frequency of sinusoid is 60 cycles per second. Suppose at Time = 0 seconds the current is at its max of 5 amperes. Write an equation expressing current in terms of time
To write an equation expressing the current in terms of time, we can use the formula for a sinusoidal function. A general form of a sinusoidal function is:
y = A * sin(2πft + φ)
Where:
y is the dependent variable (current in this case).
A is the amplitude of the function, which represents the maximum value of the current.
f is the frequency of the sinusoidal function.
t is the independent variable (time in this case).
φ is the phase shift of the function.
In this case, we are given A = 5 amperes and f = 60 cycles/second.
Since the frequency is given in cycles per second, and 1 cycle corresponds to a complete sinusoidal waveform (from 0 to 2π radians or 0 to 360 degrees), we can substitute f into the equation as:
f = 2π * 60 = 120π radians/second
Now, our equation becomes:
y = 5 * sin(120πt + φ)
To determine the phase shift (φ), we need more information. Is there any specific information given about the phase shift at Time = 0 seconds?