DC Machine Internal Characteristics Plot

In DC machines, different characteristics plots help us understand how the machine behaves under various operating conditions. These plots show the relationship between different electrical quantities.

The question asks about the internal characteristics of a DC machine. The internal characteristic curve is a plot that shows how the internally generated back EMF varies with the armature current.

Understanding DC Machine Characteristics

• Open Circuit Characteristic (OCC): This characteristic shows the relationship between the generated EMF (E₀ or E) and the field current (I_f) when the armature current (I_a) is zero (no load). It is essentially the magnetization curve of the machine.
• External Characteristic: This characteristic shows the relationship between the terminal voltage (V_t) and the load current (I_L). It reflects the voltage drop due to armature resistance and armature reaction as the load increases.
• Internal Characteristic: This characteristic shows the relationship between the generated EMF (E) and the armature current (I_a). It is obtained from the external characteristic by adding the voltage drop due to armature resistance (I_aR_a) to the terminal voltage (V_t). It accounts for the effect of armature reaction on the generated EMF but not the armature resistance drop.

Analyzing the Options

Let's look at the given options in the context of these definitions:

1. EMF induced in the armature (E) vs field current (I_f): This describes the Open Circuit Characteristic (OCC) or magnetization curve.
2. Terminal voltage (V_t) vs load current (I_L): This describes the External Characteristic.
3. Terminal voltage (V_t) vs armature current (I_a): This is closely related to the External Characteristic, as load current and armature current are directly related, especially in series or shunt machines (ignoring field current in shunt machines for simplicity in the external characteristic context). However, it still plots terminal voltage, not generated EMF.
4. EMF induced in the armature (E) vs armature current (I_a): This plot specifically shows how the internally induced EMF changes as the armature current varies, reflecting the effect of armature reaction. This matches the definition of the internal characteristic. The relationship can be expressed as:

   \(E = V_t + I_a R_a\)

   where \(E\) is the induced EMF, \(V_t\) is the terminal voltage, \(I_a\) is the armature current, and \(R_a\) is the armature resistance. The internal characteristic essentially plots the calculated \(E\) against \(I_a\).

Based on the definitions, the internal characteristic of a DC machine is plotted between the EMF induced in the armature (\(E\)) and the armature current (\(I_a\)).