The current in a 135 mH inductor changes with time as given by the equation I = bt^2 - at. If a =...

Question:

The current in a 135 mH inductor changes with time as given by the equation {eq}I = bt^2 - at {/eq}. If {eq}a = 6 \ \rm A/s {/eq} and {eq}b = 2 \ \rm A/s^2 {/eq}, ?nd the magnitude of the induced emf at t = 0.6 s.

Inductor:

An Inductor in a circuit produces back emf, due to any change in current in the circuit. The back emf of the inductor is proportional to the rate of change of current in the circuit and the value of inductance.

Answer and Explanation:

Given Data

  • Inductance, L = 135 mH = 0.135 H
  • The current in the circuit as a function of time as: {eq}I\ = bt^2\ - at{/eq}
    where {eq}a\ = 6\ A/s\\b\ = 2\ A/s^2{/eq}

Finding the magnitude of induced emf (E) at t = 0.6 s

The magnitude of induced emf is given by:

  • {eq}E\ = -L\times \dfrac{dI}{dt} {/eq}
  • {eq}E\ = -L\times \dfrac{d}{dt} ( bt^2\ - at) {/eq}
  • {eq}E\ = -L\times (2bt\ - a){/eq}
  • {eq}E\ = -0.135\times (2\times 2\times 0.6\ - 6){/eq}
  • {eq}E\ = 0.486\ V{/eq}

Learn more about this topic:

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Faraday's Law of Electromagnetic Induction: Equation and Application

from High School Physics: Help and Review

Chapter 13 / Lesson 10
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