Askiitians Tutor Team
Last Activity: 5 Months ago
To determine the terminal voltage of a 4-pole, lap-wound DC shunt generator under the given conditions, we need to follow a systematic approach. We will calculate the generated voltage (also known as the electromotive force, or EMF) and then account for the voltage drop across the armature resistance to find the terminal voltage.
Step 1: Calculate the Generated EMF
The formula for the generated EMF (E) in a DC generator is given by:
E = (Φ × Z × N × P) / (60 × A)
- Φ = useful flux in webers (0.08 Wb)
- Z = total number of armature conductors (which is equal to the number of turns in lap winding, so Z = 260)
- N = speed in revolutions per minute (1000 rpm)
- P = number of poles (4)
- A = number of parallel paths in the armature (for lap winding, A = P = 4)
Now, substituting the values into the formula:
E = (0.08 Wb × 260 × 1000 × 4) / (60 × 4)
Calculating this step-by-step:
- Numerator: 0.08 × 260 × 1000 × 4 = 83200
- Denominator: 60 × 4 = 240
- Thus, E = 83200 / 240 = 346.67 V
Step 2: Calculate the Voltage Drop Across the Armature Resistance
Next, we need to find the voltage drop across the armature resistance (I × Ra), where:
- I = armature current (55 A)
- Ra = armature resistance (0.006 ohms)
Now, calculating the voltage drop:
Voltage Drop = I × Ra = 55 A × 0.006 ohms = 0.33 V
Step 3: Determine the Terminal Voltage
The terminal voltage (Vt) can be calculated using the formula:
Vt = E - Voltage Drop
Substituting the values we calculated:
Vt = 346.67 V - 0.33 V = 346.34 V
Final Result
Therefore, the terminal voltage of the generator when running at 1000 rpm and supplying an armature current of 55 A is approximately 346.34 V.
This calculation illustrates how the generated EMF and the armature resistance interact to determine the terminal voltage in a DC shunt generator. Understanding these relationships is crucial for analyzing and designing electrical machines effectively.
