Which expression represents the instantaneous voltage according to the sinusoidal formula?

Which expression represents the instantaneous voltage according to the sinusoidal formula?

• A. Vi = Vmax × sin(ωt)
• B. Vi = Vmax × cos(ωt)
• C. Vi = Vmax × sin(-)
• D. Vi = Vmax × tan(-)

Answer: (C)

For a sinusoidal voltage, the instantaneous value follows the time dependence v(t) = Vmax sin(ωt + φ). If the reference phase is zero, this becomes Vi = Vmax sin(ωt). This form directly shows how the voltage passes through zero and rises and falls sinusoidally as time advances. The cosine form is just a phase-shifted version of the same waveform (cos(ωt) = sin(ωt + 90°)). Expressions like tan(ωt) do not describe a pure sinusoid, and sin of an undefined phase (like sin(-)) isn’t a complete representation. So the best expression for the instantaneous voltage with zero phase is Vi = Vmax × sin(ωt).

For a sinusoidal voltage, the instantaneous value follows the time dependence v(t) = Vmax sin(ωt + φ). If the reference phase is zero, this becomes Vi = Vmax sin(ωt). This form directly shows how the voltage passes through zero and rises and falls sinusoidally as time advances. The cosine form is just a phase-shifted version of the same waveform (cos(ωt) = sin(ωt + 90°)). Expressions like tan(ωt) do not describe a pure sinusoid, and sin of an undefined phase (like sin(-)) isn’t a complete representation. So the best expression for the instantaneous voltage with zero phase is Vi = Vmax × sin(ωt).