Question

2. an ac generator has 100 rectangular loops on its armature. each loop is 14 cm long and 12 cm wide. the armature rotates at 1200 rpm about an axis parallel to the long side. if the loop rotates in a uniform magnetic field of 0.20 t, which is perpendicular to the axis of rotation, what will be the maximum output voltage of this generator?

Answer 1

The maximum output voltage of this generator is approximately 201.06 V.

Step-by-step explanation:

In order to find the maximum output voltage of the generator, we need to use the formula:

V_max = N * A * B * ω

Where:

• V_max is the maximum output voltage
• N is the number of loops on the armature
• A is the area of one loop
• B is the magnetic field strength
• ω is the angular velocity of the armature

Given that there are 100 rectangular loops on the armature, each with a length of 14 cm and a width of 12 cm, and the armature rotates at 1200 rpm in a magnetic field of 0.20 T, we can calculate the maximum output voltage as follows:

N = 100 loops

A = length * width = 14 cm * 12 cm = 168 cm² = 0.0168 m²

B = 0.20 T

ω = (2π * 1200 rpm) / 60 = 40π rad/s

Now we can substitute the values into the formula:

V_max = 100 * 0.0168 m² * 0.20 T * 40π rad/s

Simplifying the expression, we find:

V_max ≈ 201.06 V

Therefore, the maximum output voltage of this generator is approximately 201.06 V.

Answer 2

The maximum output voltage of the AC generator with 100 rectangular loops, each 14 cm by 12 cm, rotating at 1200 rpm in a 0.20 T magnetic field is approximately 42.3 V.

Step-by-step explanation:

The student's question pertains to an AC generator and seeks to determine the maximum output voltage given specific parameters of the generator. The generator has 100 rectangular loops, each with a length of 14 cm and a width of 12 cm. It rotates with an angular velocity of 1200 rpm in a uniform magnetic field perpendicular to the axis of rotation. The formula used to calculate the maximum or peak output voltage (Emax) of an AC generator is:

Emax = NABw

where:
N = number of turns in the coil
A = area of a loop
B = magnetic field strength
w = angular velocity in radians per second

To find the maximum output voltage:

1. 
   
3. First, calculate the area of one loop:
4. 
   
6. A = length × width = 0.14 m × 0.12 m = 0.0168 m²
7. 
   
9. Convert the angular velocity from rpm to radians per second:
10. 
    
12. w = 1200 rpm × (2π rad/1 rev) × (1 min/60 s) = 125.66 rad/s
13. 
    
15. Use the formula to calculate Emax:
16. 
    
18. Emax = 100 × 0.0168 m² × 0.20 T × 125.66 rad/s
19. 
    
21. Emax = 42.27744 V
22. 
    
24. Therefore, the maximum output voltage is approximately 42.3 V.