Current across resistor and inductor

[verbose]

Homework Statement

I have a resistor and an inductor in series. The current across each is the same, correct? I want to know if I can use Ohm's Law to solve for current across the inductor if I know the Voltage and inductive reactance. Basically, does I = V/X_{L} ?

Homework Equations

V = IR
I = V/R

does I = V/ X_{L} ?

The Attempt at a Solution

 

[HallsofIvy]

??What do you mean by X_{L}? I can guess that V is the voltage drop, I the current and R the resistance. Is X_{L} the inductance? If so then, no, the voltage drop over an inductance is NOT given by the same equation as for a resistance. Surely you have that formula in your text?

 

[verbose]

X_{l}

by this i mean inductive reactance...sorry, it's tex syntax for X with L as a subscript. i have the habit of writing all my mathy stuff in latex syntax

 

[SGT]

by this i mean inductive reactance...sorry, it's tex syntax for X with L as a subscript. i have the habit of writing all my mathy stuff in latex syntax

Yes, I = \frac{V_L}{X_L}
Notice that X_L is dependent of the frequency of V_L

 

[Foxdove]

Homework Statement

I have a resistor and an inductor in series. The current across each is the same, correct? I want to know if I can use Ohm's Law to solve for current across the inductor if I know the Voltage and inductive reactance. Basically, does I = V/X_{L} ?

Homework Equations

V = IR
I = V/R

does I = V/ X_{L} ?

The Attempt at a Solution

Forget the problem for a minute, first let's clear up that current isn't across anything. Current flows through and voltage is established across. Like fingers on a chalk board.

 

[mplayer]

If those 2 elements are in series (the resistor and inductor) and connected to a voltage source, the current through all elements will be given by:

I = V_S / (R + X_L)


If the voltage you are talking about is the voltage across the inductor, then yes, the current through all elements will given by:

I = V_L / X_L