You wish to build a time delay circuit using a 75h inductor. you want the voltage across the inductor

option D

Explanation:

given,

inductance = L = 75 H

initial voltage (V₀) = 12 V

voltage across the inductor to fall to =  3.0 V

time taken to fall of voltage = 2.0 s

Resistance of the circuit = ?

using equation

[tex]V = V_0 e^{\dfrac{-tR}{L}}[/tex]

[tex]3 = 12 e^{\dfrac{-2 \times R}{75}}[/tex]

[tex]0.25 = e^{-0.02667 \times R}[/tex]

taking ln both side

[tex]ln (0.25) = -0.02667 \times R[/tex]

[tex]-1.3863 = -0.02667 \times R[/tex]

R = 51.97 Ω

hence, the correct answer is option D

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