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Unformatted text preview: CHAPTER 27ELECTRIC CURRENT Section 27- 1: Electric Current Problem 1. A wire carries 15 . A. How many electrons pass through the wire in each second? Solution The current is the amount of charge passing a given point in the wire, per unit time, so in one second, q I t = = = A s C. ( . )( ) . 15 1 15 The number of electrons in this amount of charge is 15 16 10 9 38 10 19 18 . . . . C C = = - Problem 2. In an ionic solution, 41 10 15 . ions, each carrying charge + 2 e , pass to the right each second, 3 6 10 15 . ions, each carrying - e , pass to the left in the same time. What is the net current? Solution The net current (taken as positive to the right) is ( . )( ) ( . )( )( ) ( . ) 41 10 2 3 6 10 1 16 10 15 1 15 1 19 + -- = -- s s C e e ( . . ) . 2 41 3 6 10 189 15 1 + =- s mA. (The factor - 1 in the negative ion current represents a drift velocity to the left.) Problem 3. A 12-V car battery is rated at 80 ampere-hours, meaning it can supply 80 A of current for 1 hour before it becomes discharged. If you accidentally leave the headlights on until the battery discharges, how much charge moves through the lights? Solution A battery rated at 80 A h can supply a net charge of q I t = = = C/s s C ( )( ) . . 80 3600 2 88 10 5 Problem 4. The electron beam that paints the image on a computer screen contains 5 0 10 6 . electrons per cm of its length. If the electrons move toward the screen at 6 0 10 7 . m/s, how much current does the beam carry? What is the direction of this current? Solution In Equation 27-2, nA is the number of charge carriers per unit length of beam, so I nAq d = = - v ( ) 5 10 6 1 cm ( . )( ) . 16 10 6 10 4 8 19 7 =- C m/s mA. This is the magnitude of the current; since electrons are negatively charged, the direction of the current is opposite to the drift velocity. Problem 5. Microbiologists measure total current due to potassium ions ( ) K + moving through a cell membrane of a rock crab neuron cell to be 30 nA. How many ions pass through the membrane each second? Solution The charge moving through the membrane each second is 30 nC. Since singly-charged ions carry one elementary charge (about 160 zC), this corresponds to 30 160 188 10 6 02 10 11 23 nC zC/ion ion ion/mol) 0.311 pmol. = = ( ) ( . ) ( . = = (See Example 27-2(a), Appendix B, and Table 1-1.) Chemical drug-testing instrumentation can detect amounts of substances this low. Problem 6. An ion channel in a cell membrane carries 2.4 pA when its open, but its only open 20% of the time. (a) What is the 2 CHAPTER 27 average current in the channel? (b) If the channel opens for 10 . ms, how many singly ionized ions pass through it in this time?...
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