Understanding DC Shunt Generator EMF Calculation

The question asks us to determine the generated electromotive force (EMF) of a DC shunt generator. A DC shunt generator is an electrical machine where the field winding is connected in parallel (shunt) with the armature winding and the load. To find the generated EMF, we need to account for the voltage drop across the armature resistance when the generator is supplying current to the load.

Let's break down the problem into manageable steps, using the provided information about the DC shunt generator, its load, and its internal resistances.

Key Parameters of the DC Shunt Generator

We are given the following values for the DC shunt generator:

• Load Power ($\text{P}_{\text{L}}$): $1.9 \text{ kW} = 1900 \text{ W}$
• Terminal Voltage ($\text{V}_{\text{t}}$): $220 \text{ V}$
• Armature Resistance ($\text{R}_{\text{a}}$): $0.5 \text{ } \Omega$
• Field Resistance ($\text{R}_{\text{sh}}$): $400 \text{ } \Omega$

Our goal is to find the generated electromotive force ($\text{E}_{\text{g}}$).

Step-by-Step Calculation of Generated EMF

1. Load Current Calculation

First, we need to determine the current supplied to the load. The load current ($\text{I}_{\text{L}}$) can be calculated using the load power and the terminal voltage.

The formula for power is: \[ \text{P}_{\text{L}} = \text{V}_{\text{t}} \times \text{I}_{\text{L}} \] Rearranging to find the load current: \[ \text{I}_{\text{L}} = \frac{\text{P}_{\text{L}}}{\text{V}_{\text{t}}} \]

Substituting the given values: \[ \text{I}_{\text{L}} = \frac{1900 \text{ W}}{220 \text{ V}} \] \[ \text{I}_{\text{L}} \approx 8.636 \text{ A} \]

2. Shunt Field Current Determination

Next, we calculate the current flowing through the shunt field winding ($\text{I}_{\text{sh}}$). Since the field winding is connected in parallel (shunt) with the armature and the load, the voltage across the field winding is the same as the terminal voltage.

Using Ohm's Law for the shunt field circuit: \[ \text{I}_{\text{sh}} = \frac{\text{V}_{\text{t}}}{\text{R}_{\text{sh}}} \]

Substituting the given values: \[ \text{I}_{\text{sh}} = \frac{220 \text{ V}}{400 \text{ } \Omega} \] \[ \text{I}_{\text{sh}} = 0.55 \text{ A} \]

3. Armature Current Calculation

In a DC shunt generator, the total current generated by the armature ($\text{I}_{\text{a}}$) is split between the load and the shunt field winding. Therefore, the armature current is the sum of the load current and the shunt field current.

The formula for armature current is: \[ \text{I}_{\text{a}} = \text{I}_{\text{L}} + \text{I}_{\text{sh}} \]

Substituting the calculated current values: \[ \text{I}_{\text{a}} = 8.636 \text{ A} + 0.55 \text{ A} \] \[ \text{I}_{\text{a}} = 9.186 \text{ A} \]

4. Armature Voltage Drop Calculation

As the armature current flows through the armature winding, there is a voltage drop across the armature's internal resistance ($\text{R}_{\text{a}}$). This voltage drop is an internal loss within the generator.

Using Ohm's Law for the armature voltage drop: \[ \text{Voltage Drop} = \text{I}_{\text{a}} \times \text{R}_{\text{a}} \]

Substituting the calculated armature current and given armature resistance: \[ \text{Voltage Drop} = 9.186 \text{ A} \times 0.5 \text{ } \Omega \] \[ \text{Voltage Drop} = 4.593 \text{ V} \]

5. Calculating the Generated EMF

The generated EMF ($\text{E}_{\text{g}}$) is the total voltage produced by the armature. This generated voltage is equal to the terminal voltage plus the voltage drop across the armature resistance. This is because the armature voltage drop is subtracted from the generated EMF to give the terminal voltage.

The formula for generated EMF in a DC shunt generator is: \[ \text{E}_{\text{g}} = \text{V}_{\text{t}} + (\text{I}_{\text{a}} \times \text{R}_{\text{a}}) \]

Substituting the terminal voltage and the calculated armature voltage drop: \[ \text{E}_{\text{g}} = 220 \text{ V} + 4.593 \text{ V} \] \[ \text{E}_{\text{g}} = 224.593 \text{ V} \]

Rounding this value to the nearest whole number, the generated EMF is approximately $225 \text{ V}$.

This step-by-step approach clearly shows how the generated EMF of the DC shunt generator is calculated by considering the load, terminal voltage, and both armature and field resistances. The calculated generated EMF is $225 \text{ V}$.