AP Physics C: Electricity and Magnetism - DC Motor Questions

📚 Quick Study Guide

⚡ DC Motor Basics: A DC motor converts electrical energy into mechanical energy using the principles of electromagnetism. 🧭 Torque: The torque ($\tau$) produced by a DC motor is proportional to the current ($I$) and the magnetic field ($B$). $\tau = N I A B sin(\theta)$, where $N$ is the number of loops, $A$ is the area of the loop, and $\theta$ is the angle between the area vector and the magnetic field. 🧲 Back EMF: As the motor rotates, it generates a back electromotive force (EMF), which opposes the applied voltage. $EMF = N B A \omega$, where $\omega$ is the angular velocity. ⚙️ Motor Speed: The speed of a DC motor is affected by the applied voltage, the back EMF, and the motor's construction. 💡 Power: The power ($P$) delivered by the motor is given by $P = \tau \omega$, where $\tau$ is the torque and $\omega$ is the angular velocity. 🌡️ Efficiency: Motor efficiency is the ratio of mechanical power output to electrical power input.

Practice Quiz

1. A DC motor with a coil of 100 turns and an area of $0.01 m^2$ is placed in a magnetic field of 0.5 T. If the current through the coil is 2 A, what is the maximum torque produced?
   1. 0.5 N·m
   2. 1.0 N·m
   3. 1.5 N·m
   4. 2.0 N·m
2. What is the primary function of the commutator in a DC motor?
   1. To increase the motor's speed
   2. To reverse the current direction periodically
   3. To reduce the magnetic field strength
   4. To decrease the back EMF
3. A DC motor is connected to a 12 V power supply. When the motor is running at its maximum speed, the back EMF is 10 V. If the armature resistance is 0.5 ohms, what is the armature current?
   1. 2 A
   2. 4 A
   3. 20 A
   4. 24 A
4. Which of the following factors does NOT affect the back EMF in a DC motor?
   1. The strength of the magnetic field
   2. The number of turns in the coil
   3. The angular velocity of the motor
   4. The applied voltage
5. How can the speed of a DC motor be increased?
   1. By decreasing the applied voltage
   2. By increasing the load on the motor
   3. By increasing the magnetic field strength
   4. By decreasing the magnetic field strength
6. A DC motor has an efficiency of 80%. If the electrical power input is 100 W, what is the mechanical power output?
   1. 20 W
   2. 80 W
   3. 100 W
   4. 120 W
7. What happens to the armature current of a DC motor when the load on the motor increases?
   1. It increases
   2. It decreases
   3. It remains constant
   4. It becomes zero