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Homework Help: Current in a solenoid (conceptual)

  1. May 2, 2016 #1
    1. The problem statement, all variables and given/known data

    There is a simple set up with a cylindrical solenoid that is connected to a battery. Suppose the solenoid has a total resistance of 0.2 ohms. If the battery were attached to a regular resistor of R=0.2 ohms instead of a solenoid, the current in the circuit would immediately achieve its maximum value the moment the switch is closed. By contrast, when the solenoid is connected to the battery, the current takes time to reach its maximum value. Explain in words why the current in the solenoid takes significant time to reach its final value.

    2. Relevant equations


    i(t) = Vb/R (1-e^(-t/(L/R)))

    3. The attempt at a solution

    I understand these two equations completely: the first one is the equation for current with a regular resister, whereas the second is the equation for current with a solenoid. Due to these equations the current through a solenoid is much more complicated to compute and doesn't only depend on the voltage and resistance like a regular resistor, but it also depends on time and inductance.
    I wrote this down, but I wasn't given credit since I just basically talked about the equations, which I understand. I've wrestled with this for a while now and I guess I can't seem to understand how I would explain why the current in the solenoid takes a significant time to reach its final value.
    I know that when the current goes through the solenoid it creates a magnetic field, which does not happen with a regular resistor. Is this magnetic field relating to time somehow?

    Thank you in advance! I'm really interested in how this happens and I can't seem to find this information out with the resources I've looked at.
  2. jcsd
  3. May 2, 2016 #2
    For the behavior of current in a solenoid (which is an inductor) you must think in terms of the magnetic field produced by a current in the form of a coil.
    the flux of the magnetic field produced is such that its rate of change produces an induced emf in the coil which opposes the cause that is the voltage being put on by the battery for sending the current.
    this effect is known as Lenze's law.
    This effect is only during the interval as the current rises from zero to its peak value as during this period the current is changing leading to change in magnetic field(flux lines)- as the current becomes steady the induced e.m.f opposite to the impressed voltage will become zero. therefore if one plots the rise of current there will be a curve which is represented by your equation.
    you can estimate this time delay by actually plotting the current with time-or consult your text book on growth of current in an inductor circuit.
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