# Questions regarding AC circuits

• Engineering
• R A V E N
In summary, the problem is that when two inductors are in a closed circuit,the voltage between the inductors will be different depending on the current flowing through the inductors. The equation that is used to calculate the current through an inductor is called Kirchoff's law, and it is based on the law of Ohm. Kirchoff's law states that the voltage between two points in a circuit is proportional to the current flowing through the circuit.

#### R A V E N

Suppose that we have a simple system like one illustrated in attachment.

If we need to find complex admittance of that system,we can write:

$$\underline{Y}=G+jB=\frac{1}{\underline{Z}}=\frac{1 }{R+jX_L}\cdot\frac{R-jX_L}{R-jX_L}=\frac{R-jX_L}{R^2+X_L^2}=\frac{R}{R^2+X_L^2}+j\frac{-X_L}{R^2+X_L^2}$$

from where we can see that it is $$B=\frac{-X_L}{R^2+X_L^2}$$,althought it is $$B=\frac{X_L}{R^2+X_L^2}$$.

Why is this "-" just neglected,what is physical explanation of that?

Or it is just hardcore mathematical laws against imperfect physical reality?

Also,is it because complex numbers are just,lets say it like this,"artificial" extension of real numbers set?

Probably the explanation is that while one physical parameter is rising(susceptance $$B$$),the other is lowering(inductive reactance $$X_L$$) and vice-versa,like it is in Faradays law of induction:

$$e=-\frac{d\phi}{dt}$$

the magnetic field which is produced by induced current(which is in turn produced by induced electromotive force $$e$$) is in oposition with the change of outer flux $$\phi$$(sorry if my technical english sounds a bit clumsy).

But what if there is capacitor instead of inductor?
In that case there is no confusion like this.

There is also a "-" when active and reactive power for system like one illustrated in attachment is calculated.

#### Attachments

• system.gif
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The second question is regarding complex power $$\underline{S}$$:

why expression $$\underline{S}=\underline{U}\;\underline{I}$$ does not give the correct result,instead of that it is used $$\underline{S}=\underline{U}\;\underline{I}^*$$ where $$\underline{I}^*$$ is complex-conjugate of $$\underline{I}$$?

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I hope I will have more luck with this one:

In given circuit:

http://img90.imageshack.us/img90/9085/clipboard05xw4.gif [Broken]

where is:

$$R_1=10\;\Omega$$, $$R_3=2,5\;\Omega$$, $$R_2=X_C=X_L=5\;\Omega$$ and $$\underline{E}=50e^{j\frac{\pi}{2}}\;V$$,

find the value of current source $$\underline{I}_S$$.

Voltage drop on $$R_3$$ is $$\underline{U}=100\;V$$.

First I calculate current trough $$R_3$$: $$\underline{I}_{R_3}=\frac{\underline{U}}{R_3}=40\;A$$.

Further,by using Superposition theorem and removing branch containing $$\underline{I}_s$$ I find that $$\underline{E}$$ produces current of $$j20$$.When I substract that value from $$\underline{I}_{R_3}$$ I get $$\underline{I}_S=(40-j20)\;V$$.

However,correct result is $$\underline{I}_S=(-10+j20)\;V$$.

What I do wrong?

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Problem 4:

Could someone explain to me how to write equations using 2nd Kirchoffs Law along the closed loop in circuit where we have mutual inductance between two inductors?

I cant comprehend this correctly at all.

Here is example circuit:

http://img125.imageshack.us/img125/4779/clipboard033mw7.jpg [Broken]

The closest I was was equation with difference in one $$+$$ instedad of $$-$$.

I need explanation here,not just equations,I already have them.

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## 1. What is an AC circuit?

An AC (alternating current) circuit is a type of electrical circuit that uses alternating current to power devices. Alternating current is a type of electrical current that periodically changes direction, usually at a frequency of 50 or 60 cycles per second.

## 2. How does an AC circuit differ from a DC circuit?

An AC circuit differs from a DC (direct current) circuit in that it uses alternating current instead of direct current. Direct current flows in only one direction, while alternating current periodically changes direction. This makes AC circuits more suitable for long-distance power transmission.

## 3. What is the difference between series and parallel AC circuits?

In a series AC circuit, all components are connected in a single loop, with the same current flowing through each component. In a parallel AC circuit, components are connected in branches, with the same voltage applied across each component. This allows for different currents to flow through each branch.

## 4. How do I calculate voltage, current, and resistance in an AC circuit?

To calculate voltage, current, and resistance in an AC circuit, you can use Ohm's law. Voltage (V) is equal to current (I) multiplied by resistance (R). V = I x R. You can also use the power formula, P = VI, to calculate power in an AC circuit.

## 5. What are some common components in AC circuits?

Some common components in AC circuits include resistors, capacitors, and inductors. These components are used to control the flow of current and voltage in the circuit. Other components, such as transformers and diodes, are also commonly used in AC circuits.