Difference Between Va(t)=√2×Vm×sin(ωt) and Va(t)=Vm∠0 in Voltage Representation

The discussion clarifies the difference between two voltage representations: Va(t) = √2 × Vm × sin(ωt) and Va(t) = Vm ∠ 0. The first equation represents the instantaneous value of a sinusoidal voltage waveform at time t, where Vm is the RMS voltage amplitude. The second expression is a polar form notation indicating the voltage magnitude Vm with a phase angle, often written as Vm∠0°, representing a phasor in complex form. Some participants interpret Va(t) = Vm ∠ 0 as a shorthand for the complex exponential form Vm × exp(jωt) or Vm × cis(ωt), where cis(θ) = cos(θ) + j sin(θ), linking the polar and exponential representations of sinusoidal voltages. The discussion emphasizes that multiplying a voltage by an angle directly is not physically meaningful; instead, the angle denotes phase in the complex plane. Euler's formula connects these forms, showing equivalence between time-domain sinusoidal signals and their phasor or complex exponential representations used in AC circuit analysis.
Summary generated by the language model.