Household electrical power in the US is provided in the form of alternating current. Typically the voltage cycles smoothly between +155.6 volts and −155.6 volts 60 times per second. Use a sinusoidal function to model voltage, V, as a function of time, t, in seconds since the voltage was at its peak.
The general equation for a sinusoidal function representing alternating current is:
V(t) = V_peak * sin(2πft + φ)
Where:
- V(t) is the voltage at time t
- V_peak is the peak voltage (in this case, 155.6 volts)
- f is the frequency of the alternating current (in this case, 60 Hz)
- φ is the phase angle (assumed to be 0 in this case)
Substitute in the given values:
V(t) = 155.6 * sin(2π(60)t)
Simplifying:
V(t) = 155.6 * sin(120πt)
Therefore, the sinusoidal function representing the voltage as a function of time is:
V(t) = 155.6 * sin(120πt)