Solving for 'b': Current in a Loop w/ Bsin(1000t+b)

[CoolDude420]

Homework Statement

steady-state current through the loop will be of the form Bsin(1000t +b). What is the phase angle 'b'? in rads

Homework Equations

The Attempt at a Solution

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The answer is meant to be 0.46rads/s. However I am getting 9.65x10^-5??
I have no idea what I did wrong.

I first converted everything into the phasor domain. Then I used voltage division to get the voltage drop across the resistor. Then I used Ohms Law to get the current through the resistor which is the same as the current through the circuit.

 

[gneill]

Check your calculation for the impedance of the inductor. The formula for the impedance of an inductor is not he same as that of a capacitor.

Don't be afraid to promote j's in the denominator to the numerator. If you have a value like $1/0.25j$, then this can become $-4j$.

You don't need to do any voltage division here. Simply sum up the impedances to find the total impedance. Then apply Ohm's law directly: $I = E/Z$ (where E is the applied potential difference across Z).

 

[CoolDude420]

Check your calculation for the impedance of the inductor. The formula for the impedance of an inductor is not he same as that of a capacitor.

Don't be afraid to promote j's in the denominator to the numerator. If you have a value like $1/0.25j$, then this can become $-4j$.

You don't need to do any voltage division here. Simply sum up the impedances to find the total impedance. Then apply Ohm's law directly: $I = E/Z$ (where E is the applied potential difference across Z).

Ah.
Finally got it. Thank you soo much.
It says in my lecture notes that inductors can be described be V = jwLI or I = 1/jwL * V
It says nothing else. How do I know like what to use when? I mean say I am converting a 2H inductance into the phasor form, how do I know what to use?

 

[gneill]

$Z_L = j \omega L$

$Z_C = \frac{1}{j \omega C}$