Question

A battery, an inductor, a resistor, and a switch are wired in series. The battery produces an emf of 12.0 V and the inductor is rated at 25.0 mH. What size resistor should be used to yield 65% of the maximum current through the inductor when the switch has been closed for 0.35 s?

Answer 1

0.075 ohm

Step-by-step explanation:

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

`i` = value of the current after time "t = 0.35 s" = 0.65
`i_(o)`

`R` = resistance of the resistor = ?

`L` = Inductance of the inductor = 25 mH = 0.025 H

`T` = Time constant of the circuit

Current at any time is given as

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

`(0.65) i_(o) = i_(o)(1 - e^{(-0.35)/(T)})`

`(0.65) = (1 - e^{(-0.35)/(T)})`

`T = 0.333` sec

Time constant is given as

`T = (L)/(R)`

`0.333 = (0.025)/(R)`

`R = 0.075` ohm