A simple generator has a square armature 9.0 cm on a side. The armature has 95 turns of 0.59-mm-diameter copper wire and rotates in a 0.800-T magnetic field. The generator is used to power a lightbulb rated at 12.0 V and 25.0 W. Part A At what rate should the generator rotate to provide 12.0 V to the bulb? Consider the resistance of the wire on the armature.

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### Understanding Generators and Their Operation

**Generator Description:**

A simple generator has a square armature measuring 9.0 cm on each side. This armature includes 95 turns of copper wire, each with a diameter of 0.59 mm, and operates in a magnetic field with a strength of 0.800 T (Tesla). The generator is designed to power a lightbulb rated at 12.0 V and 25.0 W.

**Key Parameters:**
- **Armature Dimensions:** 9.0 cm x 9.0 cm
- **Number of Turns of Copper Wire:** 95
- **Diameter of Copper Wire:** 0.59 mm
- **Magnetic Field Strength:** 0.800 T

**Application:**
- **Lightbulb Rating:** 12.0 V, 25.0 W

**Problem Statement (Part A):**

At what rate should the generator rotate to provide 12.0 V to the bulb? Consider the resistance of the wire on the armature.

**Analysis:**

To solve this, you'll need to determine multiple factors including the effective resistance due to the copper wire and required rotational speed to achieve the desired voltage. 

**Steps:**

1. **Calculate Resistance of the Copper Wire:**
   - Use the wire dimensions and material properties to find the resistance.
2. **Determine the Required Current:**
   - Using the power and voltage ratings of the lightbulb, use the formula \( P = VI \).
3. **Find the Necessary Rotational Speed:**
   - Apply Faraday’s Law of Induction to understand the relationship between rotational speed and the induced voltage.

This problem blends concepts of electromagnetism, mechanics, and electrical circuits to illustrate the practical application of a generator in powering electrical devices.

For a detailed step-by-step solution, students would typically explore concepts such as electrical resistance calculations, Faraday's Law, and apply the principles of electromagnetism. This type of problem is often encountered in advanced physics and engineering courses. 

(Note: Graphs or diagrams are not present in this image.)
Transcribed Image Text:### Understanding Generators and Their Operation **Generator Description:** A simple generator has a square armature measuring 9.0 cm on each side. This armature includes 95 turns of copper wire, each with a diameter of 0.59 mm, and operates in a magnetic field with a strength of 0.800 T (Tesla). The generator is designed to power a lightbulb rated at 12.0 V and 25.0 W. **Key Parameters:** - **Armature Dimensions:** 9.0 cm x 9.0 cm - **Number of Turns of Copper Wire:** 95 - **Diameter of Copper Wire:** 0.59 mm - **Magnetic Field Strength:** 0.800 T **Application:** - **Lightbulb Rating:** 12.0 V, 25.0 W **Problem Statement (Part A):** At what rate should the generator rotate to provide 12.0 V to the bulb? Consider the resistance of the wire on the armature. **Analysis:** To solve this, you'll need to determine multiple factors including the effective resistance due to the copper wire and required rotational speed to achieve the desired voltage. **Steps:** 1. **Calculate Resistance of the Copper Wire:** - Use the wire dimensions and material properties to find the resistance. 2. **Determine the Required Current:** - Using the power and voltage ratings of the lightbulb, use the formula \( P = VI \). 3. **Find the Necessary Rotational Speed:** - Apply Faraday’s Law of Induction to understand the relationship between rotational speed and the induced voltage. This problem blends concepts of electromagnetism, mechanics, and electrical circuits to illustrate the practical application of a generator in powering electrical devices. For a detailed step-by-step solution, students would typically explore concepts such as electrical resistance calculations, Faraday's Law, and apply the principles of electromagnetism. This type of problem is often encountered in advanced physics and engineering courses. (Note: Graphs or diagrams are not present in this image.)
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