# Homework Help: LCR circuits and phase angle

1. May 29, 2012

### Sleepy_time

1. The problem statement, all variables and given/known data
A resistor (R), capacitor (C), and inductor (L) are connected in series. What is the complex impedance, Z,
of this LCR series combination?

An AC supply of voltage V(t)=V0eiωt is applied across an LCR series combination.
Derive an expression for the current I(t) in the circuit. From your expression for I(t)
write down expressions for both the magnitude of the current and the tangent of the
phase angle between current and applied voltage.

2. Relevant equations

ZL=iωL

ZC=-i/(ωC)

ZR=R

I(t)=V(t)/Z.​

where; ω=Angular frequency of the voltage and i=√(-1).

3. The attempt at a solution
For the total impedance I got:

Z=R+i(ωL-$\frac{1}{ωC}$),​

and for the current:

I=(V0eiωt)/(R+i(ωL-$\frac{1}{ωC}$)).​

For the tangent of the phase angle it would just be the tangent of the argument of the above equation for the current? If so, I can't get it into a "nice" equation without a trig function of another trig function. Thank you for any help.

Last edited: May 29, 2012
2. May 30, 2012

### tiny-tim

Welcome to PF!

Hi Sleepy_time! Welcome to PF!
tan of the phase angle of a + ib is simply b/a

for (a+ib)/(c+id), use the tan(θ-ψ) formula

3. May 30, 2012

### Sleepy_time

Hi tiny-tim, thanks for the help. So what I got is shown in the attachment. Have I got it right?

#### Attached Files:

• ###### LCR phase question.jpg
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4. May 30, 2012

### tiny-tim

Hi Sleepy_time!

erm
An AC supply of voltage V(t)=V0eiωt

the tangent of the phase angle between current and applied voltage.​

apart from that, fine!

(remember, impedance, complex current, etc are all constants! )