DC Battery and Ideal Inductor Circuit Current

In summary, the inductor is just a piece of wire and it essentially acts like a short circuit in a dc circuit. There is no reason to assume that the current will increase without bound and in reality, unavoidable resistances elsewhere in the circuit (or in the wire itself) will limit the current. Not practically. The reason is that, practically, one would need to include the internal resistance of both the inductor, L, and the voltage source, V. Practically, it is not possible to hook up an ideal inductor to an ideal voltage source, only those inductors and voltage sources that have some small, but non-zero internal resistance. So you more accurately have an RL series circuit connected to the voltage V.
  • #1
miss photon
23
0
will there be any current in a circuit with an ideal dc battery and an ideal inductor?
 
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  • #2
Yes. The inductor is fundamentally just a piece of wire, after all. It is essentially a short circuit at dc.

- Warren
 
  • #3
chroot said:
Yes. The inductor is fundamentally just a piece of wire, after all. It is essentially a short circuit at dc.

- Warren

L di/dt=V( by Kirchoffs law).this would mean current is forever increasing infinitely. is this practically possible?
 
  • #4
What is the long-term di/dt in a dc circuit?
 
  • #5
miss photon said:
L di/dt=V( by Kirchoffs law).this would mean current is forever increasing infinitely. is this practically possible?

There is no reason to assume that the current will increase without bound. In reality, unavoidable resistances elsewhere in the circuit (or in the wire itself) will limit the current.

- Warren
 
  • #6
miss photon said:
L di/dt=V( by Kirchoffs law).this would mean current is forever increasing infinitely. is this practically possible?

not practically. the reason is that, practically, one would need to include the internal resistance of both the inductor, L, and the voltage source, V. practically, it is not possible to hook up an ideal inductor to an ideal voltage source, only those inductors and voltage sources that have some small, but non-zero internal resistance. so you more accurately have an RL series circuit connected to the voltage V.
 
  • #7
"L di/dt=V( by Kirchoffs law).this would mean current is forever increasing infinitely. is this practically possible?"

This means that the voltage across the inductor is proportional to the change in inductor current over change in time multiplied by the inductance.

In a DC circuit the (steady state) the impedance Z = jwL where w is the angular frequency or 2Pif or 6.28 times the frequency (6.28f).

When f=0 (DC case), Z=0. So there is no impedance in the inductor and it acts as a short.

If the inductor acts like a short, there is no change in current and therefore di/dt =0. so essentially it says that for a DC circuit the voltage across the inductor =0 as there is no change in current.

However saying this I do understand your frustration. If we look at V=IZ and then solve for I we get I = V/Z. If Z=0 then I = infinity. However, we understand this to mean that the inductor acts as an ideal resistor = 0 ohms (offering no resistance) and that the voltage drop across the inductor is ideally zero. So if you just had a voltage source and an inductor, it means you would short out the voltage source and high amounts of current would flow. If you had an inductor in series with a resistor it means that it is just like you only had the voltage source and the resitor in the circuit and the current would be equal to V=IR or I=V/R (so no infinite current).

So getting back to the I=V/Z delima. You have to look at it like this: in a DC circuit with an ideal inductor (no resistance), the current will be at it's maximum value i.e. the inductor is not trying to limit the current through the circuit (it just acts like a wire).

Hope this helps and I hope it is not too long of an explanation.
 

1. What is the relationship between DC battery and ideal inductor circuit current?

The relationship between DC battery and ideal inductor circuit current is defined by Ohm's Law, which states that the current flowing through a circuit is directly proportional to the voltage and inversely proportional to the resistance. In an ideal inductor circuit, the inductor behaves like a short circuit to DC current, meaning that the current will flow through the circuit without any resistance. This results in a constant current flow from the battery to the inductor.

2. How does an ideal inductor behave in a DC circuit?

In a DC circuit, an ideal inductor behaves like a short circuit, allowing the current to flow through it without any resistance. This is because inductors oppose changes in current, and in a DC circuit, there is no change in current. Therefore, an ideal inductor will have zero impedance to DC current, resulting in a constant current flow.

3. What is the effect of a DC battery on an ideal inductor in a circuit?

A DC battery will provide a constant voltage to an ideal inductor, causing a constant current flow through the inductor. This current will continue to flow until the battery is disconnected or the circuit is broken. The battery's voltage will determine the strength of the magnetic field created by the inductor, which in turn affects the inductor's behavior in the circuit.

4. Can an ideal inductor store energy in a DC circuit?

Yes, an ideal inductor can store energy in a DC circuit. When the current flows through an inductor, it creates a magnetic field around the inductor. This magnetic field stores the energy from the current, and when the current is interrupted, the magnetic field collapses, releasing the stored energy back into the circuit.

5. How does the current in a DC circuit with an ideal inductor change over time?

In a DC circuit with an ideal inductor, the current will initially rise rapidly, as there is no resistance to slow it down. However, as the magnetic field builds up around the inductor, the current will eventually reach a steady state. If the circuit is interrupted, the current will decrease rapidly as the magnetic field collapses, releasing the stored energy back into the circuit. The current will then return to zero, and the cycle will repeat when the circuit is closed again.

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