Question

You wish to build a time delay circuit using a 75H inductor. You want the voltage across the inductor to fall to 3.0V from an initial voltage of 12V in a period of 2.0s. What resistance must be used in the circuit? Select One of the Following: (a) 0.019Ω (b) 110Ω (c) 150Ω (d) 52Ω (e) 11Ω

Answer 1

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Answer 2

option D

Step-by-step 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

`V = V_0 e^{(-tR)/(L)}`

`3  = 12 e^{(-2 * R)/(75)}`

`0.25 = e^(-0.02667 * R)`

taking ln both side

`ln (0.25) = -0.02667 * R`

`-1.3863 = -0.02667 * R`

R = 51.97 Ω

hence, the correct answer is option D