# Homework Help: Calculate the total impedance of the circuit

1. Jul 21, 2011

### blueyellow

1. The problem statement, all variables and given/known data

Consider a circuit, composed of a resistance R and an inductance L in series with an AC generator providing a voltage V(t)=V(subscript 0) cos (omega*t)

calculate the total impedance of the circuit, and the phase difference between its resistive and inductive components

3. The attempt at a solution

I am totally confused about what it is asking for when it asks for the 'total impedance'. does it have anything to do with the complex impedance?

2. Jul 21, 2011

### Staff: Mentor

Yup. Every passive component (resistor, capacitor, inductor) has an impedance represented by a complex number. Resistors happen to have a zero value for the imaginary term. You're being asked to find the net impedance represented by the resistor in series with the inductor.

3. Sep 3, 2011

### blueyellow

I really don't know how to do this. I only have a day and a half before I get tested on this. Please help

4. Sep 3, 2011

### blueyellow

Z=sqrt(R^2+(X(subscript L)-X(subscript C))^2))

but how am I supposed to use that equation and is it the right equation?

5. Sep 3, 2011

### stallionx

Use for impedances the fact that

Zresistor=R
Z(subL) = jwL

V=IZ

i is same

Vo* (e**0)=[Io](e**j phi t)( R+jwl)

and the fact that

v(subL)=L(di/dt)

i(t)=I(sub0)Cos(wt+phi)

I(t)=I(sub0) (e**phi j t )

Last edited: Sep 3, 2011
6. Sep 3, 2011

### blueyellow

Z=V/I=(V0cos(omega*t))/(I0exp(phi t))?

how do I calculate the phase difference?

7. Sep 3, 2011

8. Sep 3, 2011

### blueyellow

forgot j's where?

9. Sep 3, 2011

### stallionx

phi*t*(j)

But for the solution if you want a clear explanation, I will try my best

Now

there are phasors I,V,Z ( phasors )

i,v,R ( normal i'll call them ) currents, etc

I(big I ) is in the form= Io * cos(wt+phi)

Phasor - wise it is interpreted as Io * e**(jphit)

There are impedances where denoted by Z

Z=R for resistor and ZL=jwL for an inductor, 1/(jwC) for a capacitor.

You also have the relation v(small)=L*di/dt for the inductor.

All you need is some calculus to relate knowns to unknowns.

That's all I remember from my Electrics classes, so I can only offer this much help.

Good Luck !

10. Sep 3, 2011

### tiny-tim

Last edited by a moderator: Apr 26, 2017