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Resistance Ohm s Law

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					                     KEY - Problem Set I - Resistance & Ohm’s Law

       1. A steady current of 2.4 A exists in a wire for 4.0 min.
             a. How much total charged passes by a given point in the circuit during those 4.0 min? (580
                 C)
     I  2.4A                                      Q
                                                I
                    60 sec                         t
     t  4 min            240 sec
                    1min                        Q  It  (2.4A)(240 sec)  576C  580C
              b. How many electrons would this be? (3.6E21 electrons)
                1e
     580C                 3.6 10 21 e
            1.6 10 C
                    19


                            
       2. Suppose at 20.0 C the resistance of a Platinum Resistance Thermometer is 164.2 . When
                        o

          placed in a particular solution, the resistance is 187.4 . What is the temperature of this
          solution? (aplatinum = 3.92E-3oC-1) (56.0oC)
   R  Ro 1  (T To )
     187.4  164.2 3.92 10 3 (T  20)
                   1
     1.1413  1 3.92 10 3 T  0.0784
     0.2197  3.92 10 3 T
     T  56.0 o C
       3. In a dental x-ray machine, the movement of accelerated electrons is east. The current associated
          with these electrons is in what direction: (a) east, (b) west, or (c) zero. Why?

                                       electrons
                                                            Ben Franklin guessed wrong. “He was
                                                            positive about it.”
                                         Current

       4. A small toy car draws a 0.50 mA current from a 3.0 V nickel-cadmium (nicad) battery.
             a. In 10 minutes of operation, how much charge flows through the toy car?
                                                          Q
                                                       I
     I  0.5mA  0.5 103 A                              t
                  60 sec                               Q  It  (0.5 103 A)(600 sec)
     t 10 min          600 sec
                  1min                                 Q  0.30C
              b. How much potential energy is lost by the battery?
     PE  QV  (0.30C)(3.0V)  0.90J
                                         
       5. Estimate at what temperature copper wire will have the same resistivity as tungsten does at 20oC.
                            
          (copper = 0.0068C , tungsten = 0.0045C)


       6. An electric eel touches the head and tail of a cylindrically shaped fish and applies a voltage of
          600 V across it. If a current of 0.80 A results (likely killing the prey), estimate the average
          resistivity of the fish’s flesh, assuming it is 20 cm long and 4.0 cm in diameter. (4.7 m)
     V  600V                                         L
     I  0.80A                             R
                                                      A
     R ?                                              0.20m
                                           750  
     V  IR                                          (0.02m) 2
     600V  (0.80A)R                         4.71 m
     R  750
       7. A wire 5.0 m long and 3.0 mm in diameter has a resistance of 100 . A 15 V potential difference
          is applied across wire. Find:
                            the
              a. the current in the wire.
   V  IR
     15V  (100)I
     I  0.15A
                b. The resistivity of the material.

            L
   R
            A
                   5.0m
     100  
                (0.0015m) 2
       1.4 104  m
       8. A particular application requires a 20 m length of aluminum wire to have a 0.25 m resistance at
          20OC. What must be the wire’s diameter if the resistivity of the wire at the temperature is 2.82
          x10-8 m. (0.054 m)

                                                             L
                                                      R
                                                             A
     L  20m                                                                              20m
                                                      0.25 10 3   (2.82 10 8 m)
     R  0.25m  0.25 10         3
                                                                                          r 2
     T  20 o C                                       r 2  7.18 10 4
     d  2r  ?                                       r  2.68 10 2
       2.82 108 m                                d  2r  0.054m



                                   

				
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