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Homework Help: Battery Lifetime

  1. Apr 2, 2007 #1
    1. The problem statement, all variables and given/known data

    Draw a circuit the involves a battery and two identical bulbs that will maximize the lifetime of the battery. More specifically, draw a circuit that allows you to run the lights longest

    2. Relevant equations
    P = IV
    V = IR
    Series: R = R1 + R2
    Parallel: R = 1/(1/R1 + 1/R2)

    3. The attempt at a solution

    I know that the equivalent resistance of the light bulbs in series is greater than the equivalent resistance in parallel. I also know that the battery provides a fixed emf. In series, there is a smaller current and a larger resistance than in parallel. I think that because parallel circuits have less resistance, if I put the light bulbs in parallel, then the battery life will be maximized. Does this make sense, or am I woefully lost in circuits? Thank you so much.
  2. jcsd
  3. Apr 2, 2007 #2
    The voltage is a constant determined by the battery. The battery lasts the longest when there is the least amount of power getting used. Since P=IV and the voltage drop across the entire circuit is a constant determined by the battery, then the current is the only factor left. Is the current high when there is a large or small resistance?
  4. Apr 2, 2007 #3
    If you put the bulbs in parallel, will they draw more current or less current?

    If the bulbs draw more current, will the battery be able to supply energy for a greater or lesser period of time?

    (Hint: You want to minimize the rate of energy dissipation from the battery.)

    EDIT: NotMrX has said basically the same things, a few minutes before me.
  5. Apr 2, 2007 #4
    Because V = IR, and I = V/R, then the larger current will coincide with the smaller resistance (parallel circuit). If the parallel circuit has a small resistance and larger current, then it will use up more power, so the series circuit maximizes battery life, right? Thanks.
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