Question

How long until the current reaches 63% of its maximum value in an RL circuit if the resistor is 6 ohms and the inductor is 2.1 henrys?-

Answer 1

`0.35` sec

Step-by-step explanation:

`i_(o)` = maximum value of the current

`i` = value of the current after time "t" = 0.63
`i_(o)`

`R` = resistance of the resistor = 6 ohm

`L` = Inductance of the inductor = 2.1 H

Time constant of the circuit is given as

`T = (L)/(R)`

`T = (2.1)/(6)`

`T = 0.35` sec

Using the equation

`i = i_(o)(1 - e^{(-t)/(T)})`

Inserting the values

`(0.63) i_(o) = i_(o)(1 - e^{(-t)/(0.35)})`

`(0.63) = (1 - e^{(-t)/(0.35)})`

`t = 0.35` sec