EMF equation of DC generator

The emf generated in a DC generator is the emf of one parallel path of the armature winding, found from Faraday's law.

Let

• $P$ = number of poles
• $\phi$ = flux per pole (Wb)
• $Z$ = total number of armature conductors
• $A$ = number of parallel paths ($A = P$ for lap, $A = 2$ for wave)
• $N$ = armature speed (rpm)

Derivation

Flux cut by one conductor in one revolution $= P\phi$ Wb.

Time taken for one revolution $= \dfrac{60}{N}$ s.

Average emf in one conductor:

$$e = \frac{P\phi}{60/N} = \frac{P \phi N}{60}\ \text{V}$$

Number of conductors in series in one path $= Z/A$. Emf between brushes = emf of one path:

$$E_g = \frac{P \phi N}{60} \times \frac{Z}{A} = \frac{P \phi Z N}{60 A}\ \text{V}$$

Special cases

• Lap winding ($A = P$): $E_g = \dfrac{\phi Z N}{60}$
• Wave winding ($A = 2$): $E_g = \dfrac{P \phi Z N}{120}$

For a given machine, $E_g = k \phi N$, so emf is directly proportional to flux per pole and speed.

Example: 4-pole, wave wound, $Z = 378$, $\phi = 0.02$ Wb, $N = 1000$ rpm: $E_g = \dfrac{4 \times 0.02 \times 378 \times 1000}{120} = 252$ V.