To calculate the number of poles and the useful flux per pole for the synchronous generator, we can break the problem down into manageable parts using relevant equations and information.

Given data:

• Line voltage = 460 V (rms)
• Frequency (f) = 60 Hz
• Speed (n) = 900 rpm
• Star connected generator (i.e., 3-phase system)
• Two slots per pole per phase
• Four conductors per slot

Step 1: Number of Poles

To calculate the number of poles, we can use the following relation that connects the speed of the machine, the number of poles, and the frequency of the generated voltage:

$f = \frac{P \times n}{120}$

Where:

• $f$ = frequency in Hz
• $P$ = number of poles
• $n$ = speed in rpm

Rearranging this to solve for $P$ (number of poles):

$P = \frac{120 \times f}{n}$

Substituting the given values:

$P = \frac{120 \times 60}{900} = 8 \, \text{poles}$

Step 2: Flux per Pole

To calculate the flux per pole, we need to use the relationship between the line voltage and the flux. For a star-connected synchronous generator, the line voltage ($V_L$) is related to the flux per pole ($\Phi$) by the following formula:

$V_L = 4.44 \times f \times N \times \Phi$

Where:

• $V_L$ = line voltage (460 V)
• $f$ = frequency (60 Hz)
• $N$ = total number of turns per phase
• $\Phi$ = useful flux per pole (we are solving for this)

Step 2.1: Find $N$ (total turns per phase)

We are given that the stator has:

• Two slots per pole per phase
• Four conductors per slot

Thus, the total number of conductors per pole per phase is:

$\text{Conductors per pole per phase} = 2 \times 4 = 8 \, \text{conductors}$

For a three-phase generator, the total number of turns per phase is:

$N = 8 \times \text{number of poles} = 8 \times 8 = 64 \, \text{turns per phase}$

Step 2.2: Solve for Flux per Pole

Now, we can substitute all known values into the formula for $V_L$:

$460 = 4.44 \times 60 \times 64 \times \Phi$

Rearranging for $\Phi$:

$\Phi = \frac{460}{4.44 \times 60 \times 64} \approx 0.045 \, \text{Weber}$

Final Answers:

i) Number of Poles: 8 poles
ii) Useful Flux per Pole: 0.045 Weber

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Would you like further details on any part of the solution or have any follow-up questions? Here are 5 related questions for you:

1. How does the number of poles affect the generator's speed?
2. What is the relationship between flux and induced voltage in an alternator?
3. How can you calculate the synchronous speed of a generator?
4. What are the advantages of star connection in a synchronous generator?
5. How can you calculate the total number of turns in a 3-phase generator?

Tip: Always remember that for star-connected generators, the phase voltage is related to the line voltage by a factor of $\sqrt{3}$.