Question

What is the characteristic time constant of a 27.0 mH inductor that has a resistance of 4.40 Ω?

If it is connected to a 15.0 V battery, what is the current after 15.0 ms?

Answer 1

the characteristic time constant will be given as ::

= L / R                                                           { eq.1 }

where, L = inductance = 27 x 10^-3 H

R = resistance = 4.4

inserting the values in above eq.

= (27 x 10^-3 H) / (4.4 )

= 6.13 x 10^-3 sec

If it is connected to a 15.0 V battery, then its current after 15 ms which will be given as ::

I (t) = I_max (1 - e^-t/)                                                                                     { eq.2 }

where, I_max = V / R

At t = 15 ms,

I (15 ms) = (15 V / 4.4 ) [1 - e^{-15 x 10^-3/6.13 x 10^-3}]

I = (3.4 A) (1 - e^-2.446)

I = (3.4 A) (1 - 0.086)

I = (3.4 A) (0.914)

I = 3.1 A