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Edward
Edward asked in Science & MathematicsPhysics · 11 hours ago

Circuit problem ?

Part 1 of 1:

At t=0, a 12.6V battery is connected to a series circuit containing a 9 Ω resistor and a 1.2 H inductor.

What will be the current in the circuit, a long time after the circuit is established?

Part 2 of 2:

How long will it take the current to reach 50 percent of its final value?

2 Answers

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  • oldschool
    Lv 7
    8 hours ago

    i(t) = i(∞)*(1-e^-Rt/L)  where i(∞) = 12.6V/9Ω = 1.4 and R/L = 9/1.2 = 7.5

    i(t) = 1.4 * (1 - e^-7.5t) so i(∞) = 1.4 and i = 1.4/2 = 0.7 when

    ½ = (1 - e^-7.5t) SO e^-7.5t) = 0.5  Take natural logs of both sides:

    -7.5t = LN(0.5)

    t = LN(0.5)/(-7.5) = 92.4ms 

  • oubaas
    Lv 7
    11 hours ago

    If = V/R = 12/9 = 4/3 of Amps 

    timeconstant Ƭ = L/R = 1.2/9 = 0.1333 sec 

    0.5 = 1-e^-k

    e^k = 0.5

    k*ln e = ln 0.5.....(ln e = 1)

    k = -0.693 = -t/Ƭ 

    t = 0.693*0.1333 = 0.092 sec 

     

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