Electric Generators Quiz

PDF page 1107: Electric generators induce an emf by rotating a coil in a magnetic field, as briefly discussed in Induced Emf and Magnetic Flux. We will now explore generators in more detail. Consider the following example.

PDF page 1108: zero, inducing an emf. Strategy We use Faraday’s law of induction to find the average emf induced over a time :

PDF page 1107: The generator coil shown in Figure 23.19 is rotated through one-fourth of a revolution (from to ) in 15.0 ms. The 200-turn circular coil has a 5.00 cm radius and is in a uniform 1.25 T magnetic field. What is the average emf induced?

PDF page 1107: The generator coil shown in Figure 23.19 is rotated through one-fourth of a revolution (from to ) in 15.0 ms. The 200-turn circular coil has a 5.00 cm radius and is in a uniform 1.25 T magnetic field. What is the average emf induced?

PDF page 1107: The generator coil shown in Figure 23.19 is rotated through one-fourth of a revolution (from to ) in 15.0 ms. The 200-turn circular coil has a 5.00 cm radius and is in a uniform 1.25 T magnetic field. What is the average emf induced?

PDF page 1108: FIGURE 23.19 When this generator coil is rotated through one-fourth of a revolution, the magnetic flux changes from its maximum to

PDF page 1109: FIGURE 23.20 A generator with a single rectangular coil rotated at constant angular velocity in a uniform magnetic field produces an emf

PDF page 1109: that varies sinusoidally in time. Note the generator is similar to a motor, except the shaft is rotated to produce a current rather than the other way around. Charges in the wires of the loop experience the magnetic force, because they are moving in a magnetic field. Charges in the vertical wires experience forces parallel to the wire, causing currents. But those in the top and bottom segments feel a force perpendicular to the wire, which does not cause a current. We can thus find the induced emf by considering only the side wires. Motional emf is given to be , where the velocity v is perpendicular to the magnetic field . Here the velocity is at an angle with , so that its component perpendicular to is (see Figure 23.20). Thus in this case the emf induced on each side is , and they are in the same direction. The total emf around the loop is then 23.15 This expression is valid, but it does not give emf as a function of time. To find the time dependence of emf, we assume the coil rotates at a constant angular velocity . The angle is related to angular velocity by , so that 23.16 Now, linear velocity is related to angular velocity by . Here , so that , and

PDF page 1109: that varies sinusoidally in time. Note the generator is similar to a motor, except the shaft is rotated to produce a current rather than the other way around. Charges in the wires of the loop experience the magnetic force, because they are moving in a magnetic field. Charges in the vertical wires experience forces parallel to the wire, causing currents. But those in the top and bottom segments feel a force perpendicular to the wire, which does not cause a current. We can thus find the induced emf by considering only the side wires. Motional emf is given to be , where the velocity v is perpendicular to the magnetic field . Here the velocity is at an angle with , so that its component perpendicular to is (see Figure 23.20). Thus in this case the emf induced on each side is , and they are in the same direction. The total emf around the loop is then 23.15 This expression is valid, but it does not give emf as a function of time. To find the time dependence of emf, we assume the coil rotates at a constant angular velocity . The angle is related to angular velocity by , so that 23.16 Now, linear velocity is related to angular velocity by . Here , so that , and

PDF page 1109: that varies sinusoidally in time. Note the generator is similar to a motor, except the shaft is rotated to produce a current rather than the other way around. Charges in the wires of the loop experience the magnetic force, because they are moving in a magnetic field. Charges in the vertical wires experience forces parallel to the wire, causing currents. But those in the top and bottom segments feel a force perpendicular to the wire, which does not cause a current. We can thus find the induced emf by considering only the side wires. Motional emf is given to be , where the velocity v is perpendicular to the magnetic field . Here the velocity is at an angle with , so that its component perpendicular to is (see Figure 23.20). Thus in this case the emf induced on each side is , and they are in the same direction. The total emf around the loop is then 23.15 This expression is valid, but it does not give emf as a function of time. To find the time dependence of emf, we assume the coil rotates at a constant angular velocity . The angle is related to angular velocity by , so that 23.16 Now, linear velocity is related to angular velocity by . Here , so that , and

PDF page 1108: Discussion This is a practical average value, similar to the 120 V used in household power.

PDF page 1110: generator as a function of time. is the peak emf. The period is , where is the frequency. Note that the script E stands for emf. The fact that the peak emf, , makes good sense. The greater the number of coils, the larger their area, and the stronger the field, the greater the output voltage. It is interesting that the faster the generator is spun (greater ), the greater the emf. This is noticeable on bicycle generators—at least the cheaper varieties. One of the authors as a juvenile found it amusing to ride his bicycle fast enough to burn out his lights, until he had to ride home lightless one dark night.