A series RL circuit includes a 6.05 V 6.05 V battery, a resistance of R = 0.655 Ω , R=0.655 Ω, and an inductance of L = 2.55 H. L=2.55 H. Wh

Question

A series RL circuit includes a 6.05 V 6.05 V battery, a resistance of R = 0.655 Ω , R=0.655 Ω, and an inductance of L = 2.55 H. L=2.55 H. What is the induced emf 1.43 s 1.43 s after the circuit has been closed?

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Gia Bảo 5 years 2021-09-04T19:51:30+00:00 1 Answers 8 views 0

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  1. Neala
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    2021-09-04T19:52:58+00:00
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    Answer:

    The induced emf 1.43 s after the circuit is closed is 4.19 V

    Explanation:

    The current equation in LR circuit is :

    I=\frac{V}{R} (1-e^{\frac{-Rt}{L} })    …..(1)

    Here I is current, V is source voltage, R is resistance, L is inductance and t is time.

    The induced emf is determine by the equation :

    V_{e}=L\frac{dI}{dt}

    Differentiating equation (1) with respect to time and put in above equation.

    V_{e}= L\times\frac{V}{R}\times\frac{R}{L}e^{\frac{-Rt}{L} }

    V_{e}=Ve^{\frac{-Rt}{L} }

    Substitute 6.05 volts for V, 0.655 Ω for R, 2.55 H for L and 1.43 s for t in the above equation.

    V_{e}=6.05e^{\frac{-0.655\times1.43}{2.55} }

    V_{e}=4.19\ V

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