In a shunt motor, the permanent magnet is replaced by an...

In a shunt motor, the permanent magnet is replaced by an electromagnet activated by a field coil that shunts the armature. The shunt motor shown in Fig. 33-4 has an armature resistance of 0.050? and is connected to a 120 V line. (a) What is the armature current at the starting instant, i.e., before the armature develops any back emf? (b) What starting rheostat resistance $R$, in series with the armature, will limit the starting current to 60 A ? (c) With no starting resistance, what back emf is generated when the armature current is 20 A ? (d) If this machine were running as a generator, what would be the total induced emf developed by the armature when the armature is delivering 20 A at 120 V to the shunt field and external circuit? (a) Annature curnent $=\frac{\text { Inmpessed voltage }}{\text { Ammature resistance }}=\frac{120 \mathrm{~V}}{0.050 \Omega}=2.4 \mathrm{kA}$ (b) Amature curnent $=\frac{\text { Impressed voltage }}{0.050 \Omega+R} \quad$ of $\quad 60 \mathrm{~A}=\frac{120 \mathrm{~V}}{0.050 \Omega+R}$ from which $R=2.0 \Omega$. $$ \begin{aligned} & \text { (c) } \begin{aligned} \text { Back emf } & =\text { (Impressed voltage })-(\text { Voltage drop in armature resistance }) \\ & =120 \mathrm{~V}-(20 \mathrm{~A})(0.050 \Omega)=119 \mathrm{~V}=0.12 \mathrm{kV} \end{aligned} \\ & \begin{aligned} \text { (d) Induced emf } & =(\text { Terminal voltage })+(\text { Voltage drop in armature resistance }) \\ & =120 \mathrm{~V}+(20 \mathrm{~A})(0.050 \Omega)=121 \mathrm{~V}=0.12 \mathrm{kV} \end{aligned} \end{aligned} $$

In a shunt motor, the permanent magnet is replaced by an electromagnet activated by a field coil that shunts the armature. The shunt motor shown in Fig. 33-4 has an armature resistance of 0.050? and is connected to a 120 V line. (a) What is the armature current at the starting instant, i.e., before the armature develops any back emf? (b) What starting rheostat resistance $R$, in series with the armature, will limit the starting current to 60 A ? (c) With no starting resistance, what back emf is generated when the armature current is 20 A ? (d) If this machine were running as a generator, what would be the total induced emf developed by the armature when the armature is delivering 20 A at 120 V to the shunt field and external circuit?

(a) Annature curnent $=\frac{\text { Inmpessed voltage }}{\text { Ammature resistance }}=\frac{120 \mathrm{~V}}{0.050 \Omega}=2.4 \mathrm{kA}$
(b) Amature curnent $=\frac{\text { Impressed voltage }}{0.050 \Omega+R} \quad$ of $\quad 60 \mathrm{~A}=\frac{120 \mathrm{~V}}{0.050 \Omega+R}$ from which $R=2.0 \Omega$.
$$
\begin{aligned}
& \text { (c) } \begin{aligned}
\text { Back emf } & =\text { (Impressed voltage })-(\text { Voltage drop in armature resistance }) \\
& =120 \mathrm{~V}-(20 \mathrm{~A})(0.050 \Omega)=119 \mathrm{~V}=0.12 \mathrm{kV}
\end{aligned} \\
& \begin{aligned}
\text { (d) Induced emf } & =(\text { Terminal voltage })+(\text { Voltage drop in armature resistance }) \\
& =120 \mathrm{~V}+(20 \mathrm{~A})(0.050 \Omega)=121 \mathrm{~V}=0.12 \mathrm{kV}
\end{aligned}
\end{aligned}
$$

Key Concepts

Shunt Motor Configuration

A shunt motor is a type of DC machine where the field winding (electromagnet) is connected in parallel (or shunt) with the armature winding. This configuration allows for relatively constant speed operation under varying load conditions because the field flux remains largely constant. It contrasts with series and compound motor types in its method of field excitation.

Armature Resistance

Armature resistance is the inherent electrical resistance of the motor's armature winding. This resistance affects both the starting performance and the voltage drops during operation. It is crucial in calculating parameters such as the starting current and the voltage drop across the armature, which in turn influence the back EMF and overall motor performance.

Back Electromotive Force (Back EMF)

Back EMF is the voltage generated by the rotating armature in a motor, which opposes the applied voltage. It is a key indicator of the motor’s speed and load characteristics. As the motor speeds up, back EMF increases, reducing the net voltage across the armature and thereby limiting the armature current during steady-state operation.

Starting Current and Its Limitation

At startup, the armature of a DC motor produces no back EMF because it is not yet rotating, which results in a very high initial current determined only by the applied voltage and the armature resistance. Controlling this inrush current is important to prevent damage, often by using methods like adding a starting or series rheostat to limit the current during startup.

Starting Rheostat

A starting rheostat is an external resistance connected in series with the motor’s armature during startup. Its purpose is to limit the initial surge of current by increasing the total circuit resistance, thereby protecting both the motor and the power supply. Once the motor builds up speed and the back EMF increases, the rheostat can be bypassed or gradually reduced to optimize performance.

DC Generator Operation and Induced EMF

DC machines can operate both as motors and generators. In generator mode, the induced electromotive force (EMF) in the armature is generated by mechanical input rather than electrical input. The total induced EMF is the sum of the terminal voltage and the voltage drop across the armature resistance. This principle is essential for understanding and designing applications involving energy conversion between electrical and mechanical forms.

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