Chapter 27: Problem 48
A dc motor with its rotor and field coils connected in series has an internal resistance of 3.2 \(\Omega\). When the motor is running at full load on a 120-V line, the emf in the rotor is 105 V. (a) What is the current drawn by the motor from the line? (b) What is the power delivered to the motor? (c) What is the mechanical power developed by the motor?
Short Answer
Step by step solution
Identify Known Values
Apply Ohm's Law to Find Current
Calculate Power Delivered to the Motor
Determine Mechanical Power Developed by the Motor
Unlock Step-by-Step Solutions & Ace Your Exams!
-
Full Textbook Solutions
Get detailed explanations and key concepts
-
Unlimited Al creation
Al flashcards, explanations, exams and more...
-
Ads-free access
To over 500 millions flashcards
-
Money-back guarantee
We refund you if you fail your exam.
Over 30 million students worldwide already upgrade their learning with Vaia!
Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Ohm's Law
- \( I = \frac{V}{R} \)
Always remember to ensure all units are consistent when applying Ohm's Law and in practical circuit analysis scenarios.
Electromotive force
For DC motors, the emf can be thought of as the back electromotive force, which acts against the supply voltage when the motor is in operation. This is because the motor acts like a generator when it is rotating, producing its own voltage as a response to the motion, commonly known as back emf. Understanding emf is key to calculating how much voltage is effectively applied to overcome the internal resistance and perform work.
Power Calculation
- Electrical power (\( P \)) is calculated using the formula \( P = VI \), where \( V \) is voltage and \( I \) is current.
- For mechanical power, the formula \( P_{mech} = EI \) is used, where \( E \) is the electromotive force.
Internal Resistance
It plays a vital role when analyzing circuits and can significantly affect motor performance. Increased internal resistance reduces the net voltage available for mechanical work, hence decreasing efficiency.
In the given exercise, identifying the internal resistance is crucial for calculating the current flow and the power delivered to the motor, as it enables us to precisely determine how much of the input energy is actually being converted to perform useful work.
Mechanical Power
To find the mechanical power, we use the formula\[ P_{mech} = EI \]where \( E \) is the electromotive force of the motor and \( I \) is the current. High mechanical power indicates efficient conversion, while low values may point to energy losses.
Hence, understanding mechanical power helps in evaluating motor performance, ensuring that the motor meets design specifications and operates effectively in real-world applications.