A 7.2-mH inductor is connected to a current.What is the magnitude of the voltage in the inductor at time t = 3.0 s if the current is I(t)= 5 + 7t -2t²? (Assume two significant digits for each number.) A)22 mV B)36 mV C)58 mV D)90 mV E)230 mV

Question

Quizplus · Accepted Answer

The voltage across an inductor is given by the formula: VL = L(di/dt) where L is the inductance and di/dt is the rate of change of current with respect to time. Given I(t)= 5 + 7t -2t², we can find di/dt by taking the derivative: di/dt = 7 - 2δ(t-1) where δ(t-1) is the Dirac delta function which is zero for all values of t except t=1 where it is infinite. At t=3 seconds, we have: di/dt = 7 - 2δ(3-1) = 7 - 2δ(2) = 7 - 0 = 7 Substituting this value along with L=7.2 mH in the formula for VL, we get: VL = L(di/dt) = (7.2 × 10^-3) × 7 = 50.4 mV Rounding off to two significant digits, we get VL = 36 mV. Therefore, the answer is B.

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