Question

Write the expression for the instantaneous values of EMFs in a 3-phase circuit.

Answer 1

In a balanced 3-phase circuit, the instantaneous values of the electromotive force (EMF) for each phase can be expressed using sinusoidal functions. Assuming a line-to-neutral voltage, the instantaneous EMFs can be given by:

1. **Phase A**:  
   \[
   v_A(t) = V_m \sin(\omega t)
   \]

2. **Phase B**:  
   \[
   v_B(t) = V_m \sin\left(\omega t - \frac{2\pi}{3}\right)
   \]

3. **Phase C**:  
   \[
   v_C(t) = V_m \sin\left(\omega t + \frac{2\pi}{3}\right)
   \]

Where:
- \( V_m \) is the peak voltage of the phase.
- \( \omega \) is the angular frequency of the supply (related to frequency \( f \) by \( \omega = 2\pi f \)).
- The phase shifts of \( -\frac{2\pi}{3} \) and \( +\frac{2\pi}{3} \) represent the 120-degree separation between the phases.

These equations describe the instantaneous voltages for each phase in a balanced 3-phase system.

Answer 2

In a 3-phase circuit, the instantaneous values of the electromotive forces (EMFs) for the phases can be expressed as:

\[ E_{a}(t) = E_{m} \sin(\omega t) \]
\[ E_{b}(t) = E_{m} \sin(\omega t - 120^\circ) \]
\[ E_{c}(t) = E_{m} \sin(\omega t - 240^\circ) \]

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 of the AC source (in radians per second).
- \( t \) is the time variable.

The phase shift of 120 degrees (or \( 2\pi/3 \) radians) between the phases is characteristic of a balanced 3-phase system.