What is the ratio of the slope of the 50-turn electromagnet to the slope of the 25-turn electromagnet? Show your work.
all 20 turn
1.5,6
3.0, 13
4.5, 16
6.0, 24
7.5, 30
9.0, 35
10.5, 40
12.0, 44
all 50 turn
1.5,12
3.0, 28
4.5, 33
6.0, 45
7.5, 53
9.0, 72
10.5, 77
12.0, 91
To find the ratio of the slopes of the 50-turn electromagnet to the 25-turn electromagnet, we need to compare the slopes of the 50-turn electromagnet to the slopes of the 25-turn electromagnet at corresponding input voltages.
For the 50-turn electromagnet:
Slope at 1.5V = 12
Slope at 3.0V = 28
Slope at 4.5V = 33
Slope at 6.0V = 45
Slope at 7.5V = 53
Slope at 9.0V = 72
Slope at 10.5V = 77
Slope at 12.0V = 91
For the 25-turn electromagnet:
Slope at 1.5V = 6
Slope at 3.0V = 13
Slope at 4.5V = 16
Slope at 6.0V = 24
Slope at 7.5V = 30
Slope at 9.0V = 35
Slope at 10.5V = 40
Slope at 12.0V = 44
Now we will find the ratios at each input voltage:
Ratio at 1.5V = 12/6 = 2
Ratio at 3.0V = 28/13 ≈ 2.15
Ratio at 4.5V = 33/16 ≈ 2.06
Ratio at 6.0V = 45/24 = 1.875
Ratio at 7.5V = 53/30 ≈ 1.77
Ratio at 9.0V = 72/35 ≈ 2.06
Ratio at 10.5V = 77/40 ≈ 1.93
Ratio at 12.0V = 91/44 ≈ 2.07
Therefore, the average ratio of the slope of the 50-turn electromagnet to the slope of the 25-turn electromagnet is approximately 2.
the ratio needs to be a whole number ratio or fraction, not a single digit
To find the ratio of the slopes of the 50-turn electromagnet to the 25-turn electromagnet as a whole number or fraction, we can simplify the ratios we calculated earlier.
Ratios at each input voltage:
1.5V: 12/6 = 2
3.0V: 28/13
4.5V: 33/16
6.0V: 45/24 = 15/8
7.5V: 53/30
9.0V: 72/35
10.5V: 77/40
12.0V: 91/44
To simplify these ratios further:
3.0V: 28/13 is already in its simplest form
4.5V: 33/16
7.5V: 53/30 = 53/30
9.0V: 72/35
10.5V: 77/40 = 77/40
12.0V: 91/44
Therefore, the simplified ratios of the slopes of the 50-turn electromagnet to the 25-turn electromagnet are as follows:
3.0V: 28/13 ≈ 2.15
4.5V: 33/16
7.5V: 53/30
9.0V: 72/35
10.5V: 77/40
12.0V: 91/44