calculate the armature current for a lap wound DC shunt generator delivering a terminal voltage of 200v operating at 1400 rpm and having the following specifications:

1. armature resistance: 0.5 ohms
2. number of poles: 4
3. useful flux/pole: 0.02 wb
4. number of armature conductors: 450

To calculate the armature current for a lap wound DC shunt generator, we need to follow a series of logical steps. We will use the given specifications: terminal voltage (Vt), armature resistance (Ra), speed (N), number of poles (P), useful flux per pole (Φ), and the number of armature conductors (Z). Let's break this down step by step.

Step 1: Calculate the Generated EMF (Eg)

The first step is to determine the generated electromotive force (EMF) of the generator. The formula for the generated EMF in a DC generator is given by:

Eg = (P × Φ × N × Z) / 60

Where:

• P = number of poles = 4
• Φ = useful flux per pole = 0.02 Wb
• N = speed in RPM = 1400
• Z = number of armature conductors = 450

Now, substituting the values into the formula:

Eg = (4 × 0.02 × 1400 × 450) / 60

Calculating this gives:

Eg = (4 × 0.02 × 1400 × 450) / 60 = 420 V

Step 2: Determine the Armature Current (Ia)

Next, we need to find the armature current. The relationship between the terminal voltage (Vt), generated EMF (Eg), and armature resistance (Ra) can be expressed as:

Vt = Eg - Ia × Ra

Rearranging this equation to solve for the armature current (Ia) gives us:

Ia = (Eg - Vt) / Ra

Substituting the known values:

• Eg = 420 V
• Vt = 200 V
• Ra = 0.5 ohms

Now we can calculate:

Ia = (420 V - 200 V) / 0.5 ohms

This simplifies to:

Ia = 220 V / 0.5 ohms = 440 A

Final Result

The armature current for the lap wound DC shunt generator, under the given conditions, is 440 A.

This calculation illustrates how the generated EMF and terminal voltage interact through the armature resistance to determine the current flowing through the armature. Understanding these relationships is crucial for analyzing and designing DC generators effectively.