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.

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}