Calculating Current and Phase Angle in a Series RLC Circuit

[kdrobey]

Homework Statement

A circuit consists of a 215 resistor and a 0.200 H inductor. These two elements are connected in series across a generator that has a frequency of 120 Hz and a voltage of 235 V.

(a) What is the current in the circuit?

(b) Determine the phase angle between the current and the voltage of the generator.

Homework Equations

Xl=2(pi)fL
Irms=Vrms/Xl

The Attempt at a Solution

I used the equation to get 150.796 for Xl, then i plugged that into the equation Irms=Vrms/Xl to find current, but that gave me 1.558, which was not the right answer

 

[berkeman]

Your second equation in #2 above is incomplete. The resistor and inductor are in series, so you must use their total impedance in the V = I * Z equation. Does that fix it for you?

 

[kdrobey]

I'm still not getting it. I used V=IZ. I have V, which is 235 volts right? still, i did not have I or Z. So i used Z=(square root of)R^2 +(Xl-Xc)^2, and I got .89 for Z. Then plugging back into V=IZ, (235v)=I(.89)=262.49A for current?

 

[alphysicist]

Hi kdrobey,

I'm still not getting it. I used V=IZ. I have V, which is 235 volts right? still, i did not have I or Z. So i used Z=(square root of)R^2 +(Xl-Xc)^2, and I got .89 for Z. Then plugging back into V=IZ, (235v)=I(.89)=262.49A for current?

For these series RLC problems the impedance is

$$Z=\sqrt{R^2 + (X_L - X_C)^2}$$

and so the impedance cannot be smaller than the resistance, so something is wrong there. What were the actual numbers you used to calculate Z?