# AC Circuit Theory

Discussion in 'Homework Help' started by ForgottenMemorie, Mar 26, 2008.

1. ### ForgottenMemorie Thread Starter New Member

Mar 26, 2008
2
0
Im new i hope you can help. If i can see the process on how to solve this, i will be able to do my other questions by myself.

Question

A circuit consists of a resistor of 2 ohms connected in series with a pure inductance and a pure capacitance.

The value of the inductance is 130ųH and the capacitance is 0.5ųF.

The circuit is connected across a 1< 0° volt AC 100kHz supply.

Calculate.

1. The magnitude of the current flowing in the circuit

2. The phase angle of the current relative to the voltage (assume the voltage is the reference phase)

2. ### recca02 Senior Member

Apr 2, 2007
1,211
0
Thats a very bold question...

capacitive reactance = Xc= 0.5ųF x frequency
Inductive reactance = XL= 130ųF x frequency

add all resistance and reactances in series (and for parallel do the same you do for resistances in parallel)...remember we are dealing with AC here and hence it will be solved in either polar or rectangular form.
rectangular form
so total impedance Z = R + j(XL - Xc)

I = V/Z

you will need to learn a little about how mathematical operations are done on complex numbers or polar forms....google them...
the angle you get in I in polar form(I<phi) will be the phase difference.

3. ### silvrstring Active Member

Mar 27, 2008
159
0
Your capacitive reactance will be 1/(2pi*frequency*capacitance), and your inductive reactance will be XL=2pi*frequency*inductance. Everything else Recca said is right. They probably made a typo. Then find impedance Z as Recca said.

Before you can find I=V/Z, it might be easier if you convert Z to polar form. If Zrect=R+jX, and you want to convert to Zpolar, Zpolar=sqrt(R^2+X^2) with angle theta = inverseTan(X/R).

Divide E by Z as usual. Subtract denominator angle from numerator angle. You're done.

I suggest you take Recca's advice. Understanding complex numbers, both rectangular and polar form, will make your life much easier.

4. ### hgmjr Moderator

Jan 28, 2005
9,030
214
Here is a link to the AAC ebook on complex numbers. Read up on this and then see if you can take a stab at your assignment.

hgmjr