A 4-pole generator having wave wound armature winding has 60 slots, each slot containing 20 conductors. What will be voltage generated in the machine when driven at 1000 rpm assuming the flux per pole to be 5 mWb?

EMF equation of DC Machine:

When the armature conductor rotates in a stationary magnetic field then EMF is induced in the armature.

Assumption:

ϕ = useful flux per pole in webers

P = number of poles

Z = total number of armature conductor

n = speed of rotation in rms 

A = number of parallel paths

Hence, Z/A = number of armature conductors in series for each parallel path

Since the flux per pole is ϕ, therefore conductor cuts the flux Pϕ in one revolution,

Hence, Generated Voltage (E_g) = \(\frac{Pϕ}{T}\)

Where, (T = 1/n) is the time taken for one revolution in sec.

∴ (Eg) = Pϕn

The generated voltage is determined by the number of armature conductors in series in any one path between the brushes.

Therefore Total Voltage generated is given by,

E_g = (Average voltage per conductor) × (Number of conductor per parallel path)

Hence, E_g = Pnϕ × Z/A .... (1)

If N is speed in RPM,

∴ n = N/60 .... (2)

From equation (1) & (2),

\(E_g=\frac{P\phi ZN}{60A}\)

For Wave Winding: A = 2

For Lap Winding: A = P

Application:

Given,

P = 4

slot = 60 & slot/conductor = 20

∴ Condctor (Z) = 60 × 20 = 1200

N = 1000 RPM

ϕ = 5 mWb

A = 2 (Given wave winding)

From above concept,

\(E_g=\frac{P\phi ZN}{60A}=\frac{4\times 5\times 10^{-3}\times 1200\times 1000}{120}\)

Hence, Generated voltage (Eg) = 200 V