# Step-by-Step Solution Given: - Number of poles (\(P\)) = 6 - Speed (\(N\)) = 600 rpm - Type of winding = Lap winding - Number of slots = 90 - Turns per coil = 4 - Generated emf (\(E\)) = 288 V We are to find **flux per pole (\(\phi\))**. --- ## 1. **Find the Total Number of Conductors (\(Z\)):** Each slot contains one coil. Each coil = 4 turns ⇒ Each turn = 2 conductors (one up, one down). \[ \text{Total coils} = \text{Number of slots} = 90 \] \[ \text{Conductors per coil} = 4 \text{ turns} \times 2 = 8 \] \[ Z = \text{Total conductors} = \text{Number of coils} \times \text{Conductors per coil} \] \[ Z = 90 \times 8 = 720 \] --- ## 2. **Find the Number of Parallel Paths (\(A\)):** - For lap winding: \(A = P\) - \(A = 6\) --- ## 3. **Emf Equation for DC Generator:** \E = \frac{P \phi Z N}{60A} \] Given: \(E = 288\) V, \(P = 6\), \(Z = 720\), \(N = 600\), \(A = 6\) --- ## 4. **Substitute Values and Solve for \(\phi\):** Plugging in the values: \[ 288 = \frac{6 \times \phi \times 720 \times 600}{60 \times 6} \] First, simplify denominator: \[ 60 \times 6 = 360 \] Now numerator: \[ 6 \times 720 \times 600 = 6 \times 432,000 = 2,592,000 \] So: \[ 288 = \frac{2,592,000 \times \phi}{360} \] Multiply both sides by 360: \[ 288 \times 360 = 2,592,000 \phi \] \[ 103,680 = 2,592,000 \phi \] \[ \phi = \frac{103,680}{2,592,000} \] \[ \phi = .04 \, \text{Weber} \] --- ## 5. **Final Answer** \[ \boxed{.04 \ \text{Weber per pole}} \] --- ### **Summary Table** | Quantity | Value | |------------------|---------------| | Number of Poles (\(P\)) | 6 | | Speed (\(N\)) | 600 rpm | | Number of slots | 90 | | Turns per coil | 4 | | Conductors (\(Z\)) | 720 | | Parallel paths (\(A\)) | 6 | | Generated emf (\(E\)) | 288 V | | **Flux per pole (\(\phi\))** | **.04 Weber** | --- **Explanation:** We used the standard DC generator emf formula, calculated the total number of armature conductors, and solved for the required flux per pole.