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Аxis S I (induced)

Аxis S I (induced)

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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A simple generator can be made by attaching a square armature to the axle of your hamster’s exercise wheel, where the armature turns between the poles of a permanent magnet. You wish to use this device to operate a reading light (not shown) that requires a peak voltage of 15V and power of 25W. The magnetic field has strength B = 0.50 T, the square armature has sides of 10cm, and it contains 100 turns of wire. The bulb plus armature wire have a total resistance of 7Ω in the circuit.

 

a) What is the peak magnetic flux through the square armature as it turns, and at what point in the revolution does this happen? 

b) ) How fast in revolutions per minute does the hamster have to run to produce the 15V peak output?(Hint: recall that ω = 2π f.)

### Educational Resource on Electromagnetic Induction #### Explanation of the Diagram: **Image Description:** The figure consists of two parts: an illustration of a rodent in a wheel and a detailed schematic showing the concept of electromagnetic induction in a rotating conductive loop within a magnetic field. **Left Image: Rodent in a Wheel** - This part depicts a rodent, likely a mouse or a hamster, running inside a wheel. This visual analogy helps illustrate the concept of rotational motion, which is central to understanding electromagnetic induction. **Right Image: Schematic of Electromagnetic Induction** - **Components:** - **Magnetic Field (\(\mathbf{B}\)):** Represented by straight blue lines running horizontally from the North (N) to the South (S) poles of a magnet. - **Conductive Loop:** Shown as a flat rectangular loop \(abcd\) rotating about an axis. - **Points in the Loop:** - **a, b, c, d:** Points on the loop with "a" and "b" at the top and "c" and "d" at the bottom. - **Velocity (\(\mathbf{v}\)):** Indicated by green arrows on the sides of the loop, showing the direction in which the sides of the loop are moving within the magnetic field. - **Induced Current (\(I\)):** This is illustrated by an arrow along the side 'cd' to denote the direction of current flow induced by the rotating loop. - **Angles:** - **\(\theta\):** The angle between the plane of the loop and the magnetic field direction. The vertical plane has \(\theta_1\) and the horizontal position has \(\theta_1 - 90^\circ\). - **Rotation:** - The loop is depicted as rotating around an axis perpendicular to the direction of the magnetic field. - As the loop rotates, the sides 'ab' and 'cd' move up and down through the magnetic field lines. **Induction Process:** - When the loop rotates in the magnetic field, the motion of the conductive wire through the magnetic field lines causes an electromotive force (EMF) to be induced in the loop. - This induced EMF generates a current (denoted as \(I_{\text{induced}}\)) through the conductive material of the loop. **Interaction of Velocity and Magnetic Field:
Transcribed Image Text:### Educational Resource on Electromagnetic Induction #### Explanation of the Diagram: **Image Description:** The figure consists of two parts: an illustration of a rodent in a wheel and a detailed schematic showing the concept of electromagnetic induction in a rotating conductive loop within a magnetic field. **Left Image: Rodent in a Wheel** - This part depicts a rodent, likely a mouse or a hamster, running inside a wheel. This visual analogy helps illustrate the concept of rotational motion, which is central to understanding electromagnetic induction. **Right Image: Schematic of Electromagnetic Induction** - **Components:** - **Magnetic Field (\(\mathbf{B}\)):** Represented by straight blue lines running horizontally from the North (N) to the South (S) poles of a magnet. - **Conductive Loop:** Shown as a flat rectangular loop \(abcd\) rotating about an axis. - **Points in the Loop:** - **a, b, c, d:** Points on the loop with "a" and "b" at the top and "c" and "d" at the bottom. - **Velocity (\(\mathbf{v}\)):** Indicated by green arrows on the sides of the loop, showing the direction in which the sides of the loop are moving within the magnetic field. - **Induced Current (\(I\)):** This is illustrated by an arrow along the side 'cd' to denote the direction of current flow induced by the rotating loop. - **Angles:** - **\(\theta\):** The angle between the plane of the loop and the magnetic field direction. The vertical plane has \(\theta_1\) and the horizontal position has \(\theta_1 - 90^\circ\). - **Rotation:** - The loop is depicted as rotating around an axis perpendicular to the direction of the magnetic field. - As the loop rotates, the sides 'ab' and 'cd' move up and down through the magnetic field lines. **Induction Process:** - When the loop rotates in the magnetic field, the motion of the conductive wire through the magnetic field lines causes an electromotive force (EMF) to be induced in the loop. - This induced EMF generates a current (denoted as \(I_{\text{induced}}\)) through the conductive material of the loop. **Interaction of Velocity and Magnetic Field:
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