Electrical Engineering ⇒ Topic : Sinusoidal Alternating Voltage and Current

Sinusoidal Alternating Voltage and Current

Commercial alternators produce sinusoidal alternating voltage i.e. alternating voltage is a sine wave. A sinusoidal alternating voltage can be produced (For proof, refer to Art.) by rotating a coil with a constant angular velocity (say co rad/sec) in a uniform magnetic field. The sinusoidal alternating voltage can be *expressed by the equation

                     v = V_m sin ωt

where           v = Instantaneous value of alternating voltage

                   V_m= Max. value of alternating voltage

                    ω = Angular velocity of the coil

Sinusoidal voltages always produce sinusoidal currents, unless the circuit is non-linear.

Therefore, a sinusoidal current can be expressed in the same way as voltage i.e. i = I_m sin ωt Fig. a (i) shows the waveform of sinusoidal voltage whereas Fig. a (ii) shows the waveform of sinusoidal current. Note that sinusoidal voltage or current not only changes direction at regular intervals but the magnitude is also changing continuously.

                                                                                      figure (a)

Note. An alternating current can also be represented as a cosine funct on of time viz, i = I_m cos ωt .. Similarly, alternating voltage can be represented as  v = V_m cos ωt.