What is the differential equation governing the growth of current in the circuit as a function of time after t=0? express the right-hand sid

Question

What is the differential equation governing the growth of current in the circuit as a function of time after t=0? express the right-hand side of the differential equation for di(t)dt in terms of i(t), vb, r, and l?

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bonexptip 3 years 2021-08-11T03:50:42+00:00 1 Answers 206 views 0

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  1. Dau
    -1
    2021-08-11T03:52:41+00:00
    Reply

    Answer:

    v_{b}=ir+L\frac{di}{dt}

    Explanation:

    A differential equation that contain a term with di(t)/dt is in a RL circuit. Here we have

    v_{b}=v_{r}+v_{i}

    where vr is the voltage in the resistance, vi is the voltage in the inductance and vb is the source voltage. But also we have that

    v_{r}=ir\\v_{i}=L\frac{di}{dt}

    where L is the inductance of the circuit, r is the resistance an i is the current. By replacing we have the differential equation

    v_{b}=ir+L\frac{di}{dt}

    I hope this is useful for you

    regards

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