2. A \( 220 \mathrm{~V}, 2500 \mathrm{rpm} \), shunt d.c motor has an armature resistance of \( 0.4 \Omega \), is to be used for crasher machine operation. This motor should meet the following requirements; a. Three step resistors is to be used to limit the starting current, b. For quick and smooth stoppage, the dynamic braking should be used, c. This motor is to be used for constant torque drive of the crasher. d. Motor must be safe i. Draw main and control circuit diagram of an automatic dc motor starter of the above motor and include speed control. ii. From the main and control circuit diagrams, show the responsible device(s) for each major function of the dc motor starter, speed control and brake operation.

```markdown Below is the step‐by‐step solution with the required circuit diagrams and function explanations. --- **1. Main Circuit Diagram** For a shunt DC motor with automatic starter, three–step starting resistors, dynamic braking and speed control, the main circuit is arranged as follows: - The armature winding, with resistance \( R_a = 0.4\,\Omega \), is supplied from a DC source (obtained from a 220 V AC supply through a rectifier or DC supply). - A resistor bank (three resistors arranged in steps) is connected in series with the armature. Initially, the entire resistor bank is in circuit to limit the starting current. - As the motor speeds up, contactors (automatically actuated switching devices) successively bypass portions of these resistors. Typically, three sets of auxiliary contacts “step‐off” the resistors one at a time. - A field winding is connected in parallel (shunt connection) across the supply. - For dynamic braking, a braking resistor and a reversing contactor (or dynamic brake contactor) are provided. When braking is desired, the main contactor opens the supply path and a separate contactor connects the braking resistor across the armature so that the motor acts as a generator and the energy is dissipated in the resistor. - Speed control (constant torque drive) is implemented by a control device (e.g., a variable resistor network or an electronic controller) that adjusts the effective voltage (or armature circuit voltage) supplied to the motor. An example schematic diagram (main circuit) is as shown below: +-----------------------+ | DC Supply | | (220 V DC) | +-----------+-----------+ | | +------+------+ | Main Contactor | +------+------+ | +-------------+-------------+ | | [Three–step Starting Resistor Bank] | (R1, R2, R3 in series) +-------------+-------------+ | +-----+-----+ | Armature | \( R_a = 0.4\,\Omega \) +-----+-----+ | +------> To dynamic braking circuit (when engaged) | | Ground Simultaneously, the Motor Field is connected in shunt: +---- Field Winding ----+ | | | | +----------+-----------+ | Ground For dynamic braking, a separate circuit is provided: When braking is commanded: ---------------------------------- [Dynamic Brake Contactor] closes | +----------+-----------+ | Braking Resistor \( R_b \) | +----------+-----------+ | +----+----+ | Armature | +----+----+ | Ground ---------------------------------- In this configuration, when the dynamic brake contactor is actuated, the armature’s terminals are connected across the braking resistor via the closed loop. --- **2. Control Circuit Diagram** The control circuit is responsible for: - Initiating the starter sequence, - Managing the stepping off of the starting resistor bank, - Supervising the dynamic brake operation, - Providing speed control. A typical control circuit diagram is as follows: +------------------------------------------------+ | Control Power Supply (e.g., 220 V AC through | | a transformer and rectifier to obtain | | appropriate control voltage) | +------------------------------------------------+ | +--------+---------+ | Start Pushbutton | +--------+---------+ | [Control Relay Coil] | ----------------+---------------- | | | | [Auxiliary Contacts] | | | | | -- For Resistor Bypass -- | | | -- For Dynamic Brake Actuation -- | | | [Speed Control Unit] | (Potentiometer / | electronic controller) v +-------------------+ | Main Contactors | +-------------------+ | (Activates main circuit) Key points in the control circuit: - **Start/Stop Pushbuttons:** Allow the operator to start or stop the motor. - **Control Relay/Timer:** Holds the control logic to sequentially energize auxiliary contacts. - **Auxiliary Contacts:** Manage the sequential bypass of the three-step starting resistors. When the motor speed increases, these contacts close one by one. - **Speed Control Unit:** This unit (which could be a variable resistor for manual control or an electronic controller for automatic speed feedback) adjusts the voltage applied to the motor for constant torque conditions. - **Brake Control Relay:** When an emergency stop is needed, this relay actuates the dynamic brake contactor. It disconnects the supply to the motor and connects the braking resistor across the armature. --- **3. Responsible Devices and Their Functions** From the diagrams above, the functions and their responsible devices are as follows: - **Starting Resistor (Current Limiting):** - **Device(s):** The three resistors \( R_1, R_2, \) and \( R_3 \) arranged in a resistor bank. - **Operation:** They are initially in series with the armature to limit the starting current. As the motor reaches set speed increments, auxiliary contacts (controlled by the control relay/timer) bypass these resistors step-by-step. - **Speed Control:** - **Device(s):** The Speed Control Unit, which consists of a variable resistor/potentiometer or an electronic controller. - **Operation:** It adjusts the effective voltage across the motor’s armature. For a constant torque drive, maintaining proper voltage levels is critical; the speed control unit ensures that the applied voltage is in accordance with the load requirements of the crasher machine. - **Dynamic Braking:** - **Device(s):** The Dynamic Brake Contactor and Braking Resistor \( R_b \). - **Operation:** When a quick and smooth stoppage is required, the dynamic brake contactor disconnects the motor from the DC supply and connects the braking resistor across the armature. The motor, acting as a generator, dissipates its kinetic energy in the resistor, thus producing dynamic braking. - **Safety:** - **Device(s):** Overload relays, Stop Pushbutton, Control Relays and auxiliary contacts. - **Operation:** These devices ensure that the motor does not run under unsafe conditions. The control circuit isolates the motor from the supply during overload or emergency stops and controls the proper sequencing of starting, running, and braking. --- This completes the step-by-step circuit design and the description of the responsible devices for each major function in the DC motor starter system. ```