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 #5
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Jul 25, 2023
 #2
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In physics, Ohm's law says that current through a wire, I, is directly proportional to voltage, V, and inversely proportional to resistance, R:
I = V/R  
It's also true that resistance is directly proportional to the length of the wire.  We have a piece of wire.  We pass 60 volts through this wire and measure 200 milliamps of current.  If I cut the wire in half and pass 400 volts through it, how many milliamps of current will I measure?
   

 

We begin with the basic V = IR from which R = V / I and I = V / R    

 

V is in Volts.   I is in Amperes.   R is in Ohms.   

 

V = 60 Volts   

I  = 200 mA = 0.2 Amp  

                                                                R  =  V / I  

                                                                R  =  60 / 0.2  

                                                                R  =  300 Ohms   

When you cut the wire in half,   

the resistance of one piece of   

it is half of what the total was.  

 

New V = 400 Volts   

New R = 150 Ohms  

                                                                I  =  V / R    

                                                                I  =  400 / 150  

                                                                I  =  2.6667 Amps  

There are 1000 mA per Amp, thus          I  =  2666.7 mA  

.

Jul 25, 2023
 #2
avatar+2151 
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This is my "negative money" answer. 

I answered this problem a week ago. 

This is a copy / paste of that answer.    

 

Alice and Bob each have a certain amount of money. If Alice receives n dollars from Bob, then she will have 4 times as much money as Bob. If, on the other hand, she gives n dollars to Bob, then she will have 8 times as much money as Bob. If neither gives the other any money, what is the ratio of the amount of money Alice has to the amount Bob has?    

 

                                        (A + n)  =  4 • (B – n)   

                                         A + n    =  4B – 4n    

                                         A – 4B  =  –5n                   (1)    

 

                                         (A – n)  =  8 • (B + n)   

                                          A – n    =  8B + 8n   

                                          A – 8B  =  9n                    (2)   

Multiply both sides  

of (1) by 9                        9A – 36B  =  –45n              (3)    

 

Multiply both sides  

of (2) by 5                        5A – 40B  =    45n              (4)      

 

Add (3) and (4)               14A – 76B  =  0   

 

Add 76B to both sides               14A  =  76B   

 

Divide both sides by 76B   

                                                  14A          1    

                                                  ––––   =   ––    

                                                  76B           1                       

 

Multiply both sides by 76/14    

                                                      A          76                         38

                                                    –––   =   –––   reduces to   –––   

                                                      B          14                          7   

 

It works if you accept the  

concept of negative money.  

That is, n must equal –2 dollars.  

 

Say Alice has 38 and Bob has 7        

                                                     (38 + n)  =  4 • (7 – n)     

                                                      38 + n   =  28 – 4n    

                                                             5n  =  –10     

                                                               n  =  –2       

and               

                                                     (38 – n)  =  8 • (7 + n)    

                                                      38 – n   =  56 + 8n      

                                                          –9n   =  18    

                                                               n  =  –2       

.

Jul 25, 2023
Jul 24, 2023

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