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- Thread starter bubblewrap
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In summary, the coil in an AC circuit tries to generate enough current to offset the main current, but in a DC circuit, the inductance tries to hinder the current from changing. When you increase the magnitude of the voltage, the total emf goes over zero, and when you lower the voltage, the current decreases back to its original value.

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- #2

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- An inductance (coil) generates EMF proportional to the
*change*in current [tex]E = -L\frac{\mathrm{dI}}{\mathrm{dt} }[/tex] In a DC circuit this means that the inductance tries to*hinder*the current from changing. - In an AC circuit the current is trying to change all the rime and the inductance tries to resist. And the faster the current tries to change, the more the inductance resists. Therefore the
*reactance*of an inductance is [tex]Z_{L}=\omega L[/tex]

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I'm sure you did a nice explanation but I'm still a bit confused

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Read:bubblewrap said:And because in the textbooks you derive the current of the AC circuit by equaling the voltage from the battery and the emf induced from a coil; What happens when this is not true? -- Can you make it so that one is bigger than the other?

I'm sure you did a nice explanation but I'm still a bit confused

http://en.wikipedia.org/wiki/Kirchhoff's_circuit_laws

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bubblewrap said:Sorry for not stating my questions properly, I was asking about the magnitude of the emf, how can it equal the voltage in the AC circuit but cannot in the DC circuit? And because in the textbooks you derive the current of the AC circuit by equaling the voltage from the battery and the emf induced from a coil; What happens when this is not true?

Well, in a DC circuit, as I said earlier, the inductance tries to hinder the current from changing. It cannot, however, do it fully, since if the current did change, the back EMF would be zero. Thus, the current will increase until it is limited by the resistive losses in the circuit.

I suggest you draw a circuit with a battery, an inductance and a resistor in it.Start with a zero current and solve the differential equation, it will show you what happens.

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##\vec{\nabla} \times \vec{E}=-\partial_t \vec{B},##

from which in the quasistationary limit Eq. (2) in posting #2 is derives. Kirchhoff's Law tells you that the equation for the current reads

$$L \dot{I}+R I=U,$$

where $$U=\text{const}$$ is the voltage of the battery. We assume that at the beginning ##I(0)=0##. Then you turn the switch, and the equation holds.

It's pretty easy to solve. First there's obviously a particular solution, ##I=I_{\infty}=\text{const}##. Plugging this ansatz into the equation you get

$$I_{\infty}=\frac{U}{R}.$$

To find the general solution, make the ansatz

$$I(t)=I_{\infty} + i(t).$$

Plugging this in gives the homogeneous equation

$$L \dot{i}+R I=0$$

with the general solution

$$i(t)=C \exp(-R t/L),$$

and the initial condition demancs that the integration constant is ##C=-I_{\infty}=-U/R##. So the solution reads

$$I(t)=\frac{U}{R} \left [1-\exp \left (-\frac{R}{L} t \right ) \right ].$$

So the current reaches its DC value asymptotically with a "relaxation time", ##\tau=L/R##.

An RLC circuit is an electrical circuit that consists of a resistor (R), inductor (L), and capacitor (C) connected in series or in parallel. These components are used to control the flow of electric current and create specific frequency responses.

The purpose of an RLC circuit is to create a specific frequency response, such as filtering out certain frequencies or amplifying others. It can also be used as a tuning circuit in electronic devices.

An RLC circuit works by using the properties of the resistor, inductor, and capacitor to regulate the flow of current. The resistor resists the flow of current, the inductor stores energy in the form of a magnetic field, and the capacitor stores energy in the form of an electric field.

There are two main types of RLC circuits: series and parallel. In a series circuit, the components are connected in a single loop, while in a parallel circuit, the components are connected in branches. Each type has different properties and uses.

RLC circuits are used in many electronic devices, such as radios, televisions, and computers. They are also used in power systems to regulate voltage and current, and in communication systems to filter out unwanted frequencies. RLC circuits are also important in electronic engineering and research, as they allow for precise control of electrical signals.

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