Answer:
See Explanations....
Explanation:
NOTE => See attached graph.
1. 25-Turn Electromagnet
a. Strength of Batteries 1.5v vs 6.0v
6v:1.5v => 4:1 voltage ratio => That is, 6v battery is 4x voltage of 1.5v battery.
b. Ratio of Paperclips Picked Up
23clips(6v):6clips(1.5v) => 3.8clips(6v):1clip(1.5v)
That is, the 6 volt battery-EM picks up 3.8x more clips than the 1.5v battery-EM assuming constant number of coils given.
c. Empirical Relationship
From data given, an increase in voltage (V) produces a proportional increase in number of paperclips (C) picked up. Such is a Direct Relationahip between #Clips Picked Up and Battery Voltage.
Thus, C ∝ V => C = kV => k = C/V
Therefore, for k₁ = k₂ => C₁/V₁ = C₂/V₂
2. 50-Turn Electromagnet
a. Ratio of turns between electromagnets.
50-Turn EM : 25-Turn EM => 2:1 ratio of turns between electromagnets
b. Ratio of Paperclips Picked UP
Between maximum voltage and minimum voltages for 50-Turn EM
=> 47 clips (6v) : 13 clips (1.5v) => 3.6:1 ratio...
That is, the 6v battery-EM, on the average, picks up 3.6x more clips than the 1.5v battery-EM given 50-Turn EM.
3. Doubling number of coils:
Doubling the number of coils, on the average, doubles the number of clips picked up by either electromagnet.
Voltage 50-Turn EM 25-Turn EM Pick Up Ratio
1.5v 13 6 2:1
3.0v 26 12 2:1
4.5v 31 15.5 2:1
6.0v 47 23 2:1
4. Doubling Voltages:
Doubling voltage doubles the number of clips picked up by a given electromagnet regardless of the number of coils associated with magnet.
25-Turn EM Voltage Clips Pkd UP
1.5v 6
3.0v 12
Double voltage => Doubles # clips picked up*
50-Turn EM Voltage Clips Pkd UP
1.5v 13
3.0v 26
Double voltage => Doubles # clips picked up*
*Double Voltage => Double #clips picked up regardless of number of coil turns in electromagnet.
5. Predicting number of clips for 7.5v battery-EM
Using linear trendline equations shown on attached graphs...
#clips 50-Turn EM = 7.1333V + 2.5 = 7.1333(7.5) + 2.5 ≅ 56 clips
#clips 25-Turn EM = 3.6333V + 0.5 = 3.6333(7.5) + 0.5 ≅ 27 clips
Overall => 2:1 ratio of clips between 50-Turn EM and 25-Turn EM
6. Slope values based upon trendline equations shown on attached graphs are ...
25 Turn EM => slope = 3.6333
50 Turn EM => slope = 7.1333
Approximately a 2x increase upon doubling the number of coils of electromagnet.
Predicting number of clips for 1V electromagnets:
#Clips (1volt) 25-Turn EM = 3.6333(1) + 0.5 = 3.6833 ≅ 4 clips
#Clips (1volt) 50-Turn EM = 7.1333(1) + 2.5 = 9.6333 ≅ 10 clips
Shows to be consistent with double #clips with double number of coil turns.
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