What is the Meaning of the AC Voltage of the Form Δv = 100 sin(1000t)?
📘 Given Expression
The AC voltage is given by the equation:
Δv = 100 sin(1000t)
where:
- Δv is the instantaneous voltage in volts (V)
- t is the time in seconds (s)
🔍 Analysis of the Equation
This is a sinusoidal voltage waveform, commonly used in alternating current (AC) circuits.
- Amplitude: The maximum voltage is 100 volts. This represents the peak voltage the signal reaches.
- Angular Frequency (ω): The value of 1000 in the argument of the sine function is the angular frequency in radians per second.
🔢 Finding the Frequency
Frequency (f) is related to angular frequency (ω) by the formula:
f = ω / 2π
Substituting the value:
f = 1000 / (2π) ≈ 159.15 Hz
⏱️ Calculating the Period
The period (T) is the reciprocal of the frequency:
T = 1 / f = 1 / 159.15 ≈ 0.00628 seconds = 6.28 milliseconds
✅ Final Interpretation
The voltage signal Δv = 100 sin(1000t) describes an AC waveform with:
- A peak voltage of 100 V
- A frequency of approximately 159.15 Hz
- A time period of 6.28 milliseconds