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class code: SPS22 teacher: Mr. Elert
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Physics A: Problem Set 6: Electric Current

recommended reading

Barron's Let's Review: 9.2–9.3 Electric Current
physics.info: Electric Current
Wikipedia: Electric current, Ampere

classwork

  1. The magnitude of the electric field needed to produce a spark in air (its dielectric strength) is about 3 × 106 V/m. As Benjamin Franklin showed in his famous experiment of 15 June 1752, lightning is basically a very, very large spark. A good sized bolt could travel 1 km and transfer 1000 C of charge in half a second.
    1. What voltage is needed to make a typical lightning bolt?
    2. How much current flows along its jagged path?
    3. How much energy does it deliver?
    4. What is the power of a lightning bolt?
    5. Movie trivia question: Could you power a "flux capacitor" with a lightning bolt and go Back to the Future?
    1. Just look at the units and figure it out. This is formally known as dimensional analysis.

      V = Ed
      V = (3 × 106 V/m)(1000 m)
      V = 3 × 109 V
    2. Use the definition of current.

      I = ∆q/∆t
      I = (1,000 C)(0.5 s)
      W = 2,000 A
    3. Use the definition of voltage rearranged to make work (or energy) the subject.

      W = qV
      W = (1000 C)(3 × 109 V)
      W = 3 × 1012 J

      If you know where to find them, there are other equations that work.

      E = VIt
      E = (3 × 109 V)(2000 A)(0.5 s)
      E = 3 × 1012 J
    4. Use the definition of power.

      P = E/t
      P = (3 × 1012 J) ÷ (0.5 s)
      P = 6 × 1012 W

      Once again, if you know where to find them, there are other equations that work.

      P = VI
      P = (3 × 109 V)(2000 A)
      P = 6 × 1012 W
    5. There are two types of acceptable answer to this question.

      • Yes, since 6 TW ≫ 1.21 GW.
      • No, since there is no such thing as a flux capacitor or a time machine. Back to the Future is not a documentary. It's science fiction.
  2. An average human brain has a power consumption of about 20 W.
    1. How much current flows within the brain as its neurons switch from resting potential (−70 mV) to action potential (+40 mV)? Hint: a watt is a joule per second, a volt is a joule per coulomb, and an ampere is a coulomb per second.
    2. Would you blow a fuse if you wired your brain into a 20 A circuit in a typical North American home?
    3. Movie trivia question: Could you power The Matrix using humans as batteries?
    1. It's time to play the dimensional analysis game. A watt is a joule per second, a volt is a joule per coulomb, and an ampere is a coulomb per second. This means an amp is a watt per volt and current is power over voltage.


      C  =  J/s
      s J/C

      A  =  W
      V
        I  =  P  
        V  

      Remember that the potential difference is what matters, not the potential. Also remember that mV stands for millivolt, which is 0.001 V.

      I = P/V
      I = (20 J/s)/(0.110 J/C)
      I = 182 C/s
      I = P/V
      I = (20 W)/(0.120 V)
      I = 182 A
    2. There are two types of acceptable answer to this question.

      • Yes, since 182 A ≫ 20 A.

      • No, since brains don't (and can't) make use of the current coming out of an outlet. A brain is not a piece of electrical equipment.

    3. No. Absolutely not. Your brain isn't a source of energy like a battery. It uses the chemical energy from the food we eat to keep itself running. It needs all of that energy. It doesn't have any extra leftover to run a planet-wide computer system or power an army of machines. Morpheus lied to Neo.

homework

  1. Does more electric charge flow out of a battery or into a battery when it is in use? What about when it is being recharged? Explain your reasoning.
    The charge that flows out of a battery equals the charge that flows into battery in use. Words like charging, discharging, recharging, or fully charged imply that electric charge is added or removed from a battery during normal operation. This is not what's going on. A battery is something like a "pump" that drives charge around a circuit. When a battery is powering a circuit, charges are driven out one terminal, travel around the circuit, and reenter at the other terminal. Charge cannot be created or destroyed. It can only be moved around.
  2. What happens to the electrons in a wire as they pass through a light bulb (or any other electrical device)? That is, what changes as electric current flows through a circuit?

    The electrons in a wire lose electric potential energy as they travel through the devices connected to a circuit. This lost potential energy is transformed into some other form of energy depending on the device connected. The potential energy lost by electrons as they travel through a light bulb is transformed into light, for example. In a motor, the potential energy is converted into mechanical energy. In a toaster, the lost potential energy becomes heat.

  3. What is the source of the electrons when an electric current flows through a circuit?

    The electrons in a circuit come from the wires themselves (and the other conducting components of the circuit). Wires are made of metal with lots of free electrons. When a potential difference (a voltage) is placed across the ends of a wire, the free electrons that were always there are now in motion.

  4. A typical Van de Graaff generator or Wimshurst machine used for classroom demonstrations produce electric potentials of 100,000 V or more. They make impressively large sparks that hurt like hell, but will not kill you. Household electrical outlets provide a potential difference of 120 V in the US (240 V in the UK). It almost doesn't need to be said, but one should never touch bare wires in a house or any other building. The risks are just too great. This seems like a contradiction. Why doesn't the higher voltage of a classroom demonstration come with a higher risk of death? (There are two factors at work here.)

    Outlets are also more dangerous than a classroom Van de Graaff generator or Wimshurst machine because outlets can produce more current. Current kills, not voltage. A classroom Van de Graaff generator sends out sparks that are just a few milliamps in size. Household outlets can pump out several amps of current without any problem. The difference in currents is like night and day or, more accurately, like life and death.

    Outlets are also more dangerous than a classroom Van de Graaff generator or Wimshurst machine because AC is more dangerous than DC. Van de Graaff generators produce direct current (DC) — current that flows in only one direction. Household outlets produce alternating current (AC) — current that rapidly reverses direction (60 times a second in the US, 50 times a second in the UK).

    Above a certain threshold, electric current begins to interfere with the normal electrical activity of nerve and heart cells. For nerves controlling muscles, the result is paralysis. For heart cells, the result is cardiac arrest (more specifically, ventricular fibrillation, which is not the same thing as a heart attack). During electrocution, the heart and lungs stop working. No more breathing, no more circulation, no more life. The body has a harder time dealing with alternating current, probably because AC is confused (for lack of a better word). "Am I going forward? Am I going backward? I can't make up my mind." The body can't adapt to the rapid changes as easily, which makes common household outlets more dangerous than dramatic classroom demos.