Math Problem Statement
A two pole series motor runs at 707 rpm when taking 100A at 85V and with the field coil in series. The resistance of each field is 0.03 ohms and that of the armature 0.040 ohms if the coil are connected in parallel and load torque remains constant, calculate: (a) the speed (b) the additional resistance to be inserted in series with the motor to restore the speed to 707 rpm
Solution
Let's solve this problem step-by-step.
Given Data:
-
Initial Conditions (Series Connection):
- Current,
- Voltage,
- Speed,
- Armature resistance,
- Each field coil resistance,
-
Parallel Connection:
- Field coils are connected in parallel.
- Load torque remains constant.
Step 1: Calculate Total Resistance in Series Connection
In the series connection, the total resistance is given by:
Step 2: Calculate Back EMF in Series Connection
The back EMF () in a series motor is given by:
Step 3: Speed-Torque Relationship in Series Connection
The speed of a series motor is inversely proportional to the field current when the torque is constant.
Step 4: Field Current in Parallel Connection
When field coils are in parallel, the effective resistance is: The total resistance in the parallel configuration is:
Step 5: Total Current and Field Current in Parallel Connection
Let be the total current in the parallel connection and be the field current. In parallel configuration:
Let's calculate the speed in parallel configuration and then the required resistance in series to restore speed to 707 rpm.
Step 6: Calculation
Now, let's do the detailed calculation for the required speed and resistance.
(a) New Speed Calculation
We will use the formula for speed in the series motor after reconfiguring to parallel, keeping the same torque (constant current through armature).
(b) Additional Resistance
Find additional resistance such that the effective back EMF restores the speed back to 707 rpm.
I'll proceed with the detailed numerical calculations.### Results:
-
(a) New Speed (Parallel Configuration):
The new speed of the motor when the field coils are connected in parallel is approximately 212.1 rpm. -
(b) Additional Resistance to Restore Speed to 707 rpm:
No additional resistance is needed (). This is because the field weakening effect in the parallel configuration has already resulted in a significant reduction in speed.
If you need further clarification or additional details, feel free to ask!
Related Questions:
- How does connecting field coils in series versus parallel affect motor performance?
- What is the relationship between back EMF and motor speed?
- How can the addition of external resistance help in controlling motor speed?
- What would happen to the speed if the load torque were increased?
- How do changes in voltage impact the speed and torque of a motor?
Tip: In series motors, speed is highly sensitive to changes in the field current. Reducing field strength (such as by placing coils in parallel) drastically reduces speed.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Electromechanics
Electric Circuits
Motor Speed-Torque Relationship
Resistance Calculations
Formulas
R_total_series = R_a + 2R_f
E_b = V - I * R_total_series
R_f_parallel = R_f / 2
R_total_parallel = R_a + R_f_parallel
I_f = (V - E_b) / R_f
I_total = (V - E_b) / R_total_parallel
Theorems
Speed-Torque Relationship of Series Motors
Ohm's Law
Field Weakening Effect
Suitable Grade Level
Undergraduate (Electrical Engineering)
Related Recommendation
Series Motor Analysis: Armature Current, Induced EMF, and Losses Calculation
Induced Voltage in a 4-Pole Lap-Wound Armature
Induction Motor Starting Torque Calculation for 150 kW Motor with Short-circuited Slip Rings
Starting Torque Calculation for a 150 kW, 6-Pole Induction Motor
EMF Calculation for 6-Pole Generator with Wave Winding