physics problem please help mee?

Question

Consider the circuit in Figure P20.46. Taking = 6.00 V, L = 3.00 mH, and R = 9.00 .

Figure P20.46
http://www.webassign.net/pse/p32-19.gif

(a) What is the inductive time constant of the circuit?
ms
(b) Calculate the current in the circuit 250 µs after the switch is closed.

Answer 1

Ok, that's an interesting problem, let's work :

Voltage by the resistor : I.R

Voltage by the inductive : L.dI / dt

then :

Let's call the voltage = E

E - IR - LdI / dt = 0

E - IR = LdI / dt

dt / L = dI / E - IR

So that was a differential equation, now :

t / L = -Ln(E - IR)

integrating, then we will have :

I = E / R*( 1 - e^-(R/L)t)

The inductive time constant is : L / R, always, then :

constant = 3*10^-3 / 9 = 10^-3 / 3 (s)

b) I = 6 / 9*( 1 - e^-(9/3*10^-3)*250*10^-6))

I = 2/3*(1 - e^(-0.75))

I = 2/3*( 1 - 0.75) = 0.36 Ampere

Hope that helped