An Alternating Voltage: e = 100√2 sin(100t)
This equation describes an alternating voltage, which is a voltage that changes direction periodically. Let's break down the components and understand what each part represents:
Understanding the Equation
- e: This represents the instantaneous voltage at any given time (t).
- 100√2: This is the peak voltage (or amplitude) of the alternating voltage. It represents the maximum value that the voltage reaches during one cycle.
- sin(100t): This is the sinusoidal function that describes the oscillation of the voltage.
- 100: This is the angular frequency (ω) in radians per second. It determines how fast the voltage oscillates.
- t: This represents time in seconds.
Interpreting the Equation
The equation tells us that the voltage varies sinusoidally with time. The voltage starts at zero, increases to a positive peak of 100√2 volts, then decreases back to zero, goes negative to a peak of -100√2 volts, and finally returns to zero, completing one cycle. This pattern repeats itself continuously.
Key Parameters
Here are some key parameters that can be derived from the equation:
- Peak Voltage (Vp): 100√2 volts
- Root Mean Square (RMS) Voltage (Vrms): Vp/√2 = 100 volts
- Angular Frequency (ω): 100 radians per second
- Frequency (f): ω/2π = 100/2π ≈ 15.9 Hz
- Period (T): 1/f ≈ 0.063 seconds
Applications
Alternating voltages are commonly used in power systems around the world. The equation e = 100√2 sin(100t) could represent the voltage supplied to a household outlet, for example.
Understanding the Sine Function
The sine function is a mathematical function that describes a periodic wave. In this case, the sine function ensures that the voltage oscillates smoothly and periodically.
Conclusion
The equation e = 100√2 sin(100t) concisely describes an alternating voltage with a peak voltage of 100√2 volts, an angular frequency of 100 radians per second, and a frequency of approximately 15.9 Hz. Understanding this equation allows us to analyze and predict the behavior of alternating voltage in various electrical circuits and systems.
