In a 3-phase circuit, the instantaneous values of the electromotive forces (EMFs) can be represented as sinusoidal functions. For a balanced 3-phase system, the instantaneous values of the EMFs can be expressed as:
\[
E_a(t) = E_m \sin(\omega t)
\]
\[
E_b(t) = E_m \sin\left(\omega t - \frac{2\pi}{3}\right)
\]
\[
E_c(t) = E_m \sin\left(\omega t - \frac{4\pi}{3}\right)
\]
Where:
- \( E_a(t) \), \( E_b(t) \), and \( E_c(t) \) are the instantaneous EMFs in phases A, B, and C, respectively.
- \( E_m \) is the peak value of the EMF.
- \( \omega \) is the angular frequency (in radians per second).
- \( t \) is the time.
This representation assumes a balanced system with equal magnitudes of EMF in each phase and a phase difference of \( 120^\circ \) (or \( \frac{2\pi}{3} \) radians) between each phase.