Sine Wave Voltage Calculator, Formula, Sine Wave Calculation

Sine Wave Voltage Calculator:

Enter the values of peak voltage, V_p(V), angular frequency, ω_(rad/s) and time, t_(s) to determine the value of Sine voltage, V_sine(V).

Sine Wave Voltage Formula:

Sine wave voltage is a fundamental concept in electrical engineering, particularly in alternating current (AC) systems.

It represents the voltage in a circuit that varies sinusoidally with time. This sinusoidal variation is characterized by a smooth, periodic oscillation, which is crucial for describing AC signals in power systems, audio signals, and radio waves.

The sine wave voltage can be calculated using the amplitude of the voltage (V), the angular frequency (ω), and the time variable (t).

Sine voltage, V_sine(V) in volts is calculated by the product of peak voltage, V_p(V) in volts and sin of angular frequency, ω_(rad/s) in radians per second and time, t_(s) in seconds.

Sine voltage, V_sine(V) = V_p(V) * sin(ω_(rad/s) * t_(s))

V_sine(V) = sine voltage in volts, V.

V_p(V) = peak voltage in volts, V.

ω_(rad/s) = angular frequency in radians per second, rad/s.

t_(s) = time in seconds, s.

Sine Wave Voltage Calculation:

1. Calculate the sine wave voltage at a time of 0.01 seconds for a waveform with a peak voltage of 10 volts and an angular frequency of 100 radians per second:

Given: V_p(V) = 10V, ω_(rad/s) = 100rad/s, t_(s) = 0.01s.

Sine voltage, V_sine(V) = V_p(V) * sin(ω_(rad/s) * t_(s))

V_sine(V) = 10 * sin(100 * 0.01)

V_sine(V) = 10 * sin(1)

V_sine(V) = 10 * 0.8415

V_sine(V) = 8.415V.

2. Suppose a waveform has a sine wave voltage of 4.2075 volts at a time of 0.02 seconds and an angular frequency of 50 radians per second. Calculate the peak voltage:

Given: V_sine(V) = 4.2075V, ω_(rad/s) = 50rad/s, t_(s) = 0.02s.

Sine voltage, V_sine(V) = V_p(V) * sin(ω_(rad/s) * t_(s))

V_p(V) = V_sine(V) / sin(ω_(rad/s) * t_(s))

V_p(V) = 4.2075 / sin(50 * 0.02)

V_p(V) = 4.2075 / sin(1)

V_p(V) = 4.2075 / 0.8415

V_p(V) = 5V.

Applications and Considerations:

• AC Circuit Analysis: Understanding sine wave voltages is essential for analyzing and designing AC circuits.
• Signal Processing: Sinusoidal signals are fundamental in communications and signal processing.
• Power Systems: AC power generation and distribution rely on sinusoidal waveforms for efficient energy transmission.

The sine wave explained (AC Waveform analysis)