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Math Help - Numerical Differntiation with impressed voltage equation

  1. #1
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    Numerical Differntiation with impressed voltage equation

    Problem statement:

    In a circuit with impressed voltage E(t) and inductance L, Kirchhoff's first law gives the relationship:
    E(t) = L * \frac{di}{dt} + Ri
    where R is the resistance in the circuit and i is the current. Suppose we measure the current for several values of t and obtain:
    t | i
    1.00 | 3.10
    1.01 | 3.12
    1.02 | 3.14
    1.03 | 3.18
    1.04 | 3.24

    where t is measured in seconds, i is in amperes, the inductance L is a constant 0.98 henries, and the resistance is 0.142 ohms. Approximate the voltage E(t) when t = 1.00, 1.01, 1.02, 1.03, and 1.04.

    Question:

    I have been looking at this problem for a couple of days. I am unsure of where to begin with this. Can anyone give me a hint or advice to get this problem started?
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  2. #2
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    \displaystyle \left\phantom{|}\frac{di}{dt}\right |_{t = 1} \approx \frac{i_{1.1} - i_1}{t_{1.1} - t_1}.

    Follow a similar method to approximate \displaystyle \frac{di}{dt} at the other times.
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  3. #3
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    Thanks for the help. Sometimes the simplest solutions are the hardest to figure out.
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