How to Calculate Impedance in an AC Circuit with Series Components?

[9.8m*s^-2]

Homework Statement

A 25-Ω resistance is connected in series with a 30-mH inductance and a 12-µF capacitor and are connected to a 90-V (rms) ac. If the frequency of the ac source is 500 Hz, calculate

(i) the current in the circuit.
(ii) the voltage across each element
(iii) the phase angle
(iv) the power dissipated in the circuit

Homework Equations

The Attempt at a Solution

I believe I have to begin this problem by calculating the impedance but I do not understand how to begin doing that.

Thank you.

 

[xcvxcvvc]

$$X_L=\omega L$$
$$X_C=\frac{1}{\omega C}$$
$$Z= R + i(X_L - X_C)$$

 

[Fronzbot]

Well Impedence for each element is given by the equations that xcvxcvvc gave except with one little adjustment:

$$Z_L=j\omega L$$
$$Z_C=\frac{1}{j\omega C}$$
(The ones he gave were reactance)

$$\omega$$ is the angular frequency which can be calculated by setting it equal to $$2\pi f$$

From there you can solve the circuit.

 

[xcvxcvvc]

Also, just in case you don't see it:
$$j = \sqrt{-1}$$
$$\frac{1}{j}= \frac{j}{j}\frac{1}{j} =\frac{j}{-1}=-j$$

which is why that capacitive reactance is subtracted when forming the expression for impedance.