Finding RMS current in an AC solenoid

[chinye11]

Homework Statement

A 2000 turn solenoid of length 1.50 m and diameter 5.00 cm has a dc resistance of 3.0. It is
connected to a 50 Hz, 40.0 Volt (rms) ac supply. Find the rms current in the solenoid

Homework Equations

Vind = L di/dt
Vind = Induced EMF
Ohm's Law
V-Vind = IR
L = (4pi x 10^-7)n^2 Al

Where L=self inductance and l = length

The Attempt at a Solution

This is my first time using this website and i am not sure how to get in symbols, I will do my best to be clear

I started finding the inductance.

I then used Ohm's Law: V-Vind=IR

After mathematical manipulation I got I = V/R[1-e^(Rt/L)]

My question is as regards the frequency. It seems to have no effect on the system if you use my method yet if I try to find the induced E.M.F. using Faraday's Law on the magnetic flux you will find:

Vind= 0.05 Sin(theta) I(t)
Vind= 0.05 Sin (2 pi (f) t) I(t) from theta=wt

So I was wondering if someone could explain both the concept and the calculations of the effect of the frequency. Thank You.

 

[chinye11]

Just to clarify I am aware that the current is periodic and that the frequency can help in calculating max current and other such things however, I was wondering if it was of any use in this specific question.

 

[gneill]

You've effectively got a resistor and inductor in series, and it's driven by a 50Hz AC supply. If you were to calculate the effective impedance (Z) of the resistor+inductor at the given frequency, you could apply Ohm's law to find the current: I = V/Z. The magnitude of I is what you're after.

For an inductor the impedance varies in direct proportion to the frequency.

This presumes that you've been introduced to the concept of complex impedance...

 

[chinye11]

Thanks very much I hadnt covered impedance well. I have since gone through and understand it.