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PGCIL DT Electrical 13 Aug 2021 Official Paper (NR I)

Option 4 : 200 V

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