What is the effect of an inductor on current in an AC circuit?

[dobry_den]

Homework Statement

Imagine a simple AC circuit with a voltage source and an inductor:

Determine the current going through the circuit.

Homework Equations

voltage of the source: $$v = V_m\sin{\omega}t$$
induced emf in the inductor: $$e = L\frac{di}{dt}$$

The Attempt at a Solution

By Kirchhoff's second rule, v - e = 0. What puzzles me is that this would basically mean that there's no current going through the circuit, wouldn't it? But then there would be no induced emf in the inductor, so that's probably not the case. How come there's some current going through the circuit when the induced emf opposes the source emf?

 

[nrqed]

Homework Statement

Imagine a simple AC circuit with a voltage source and an inductor:

Determine the current going through the circuit.

Homework Equations

voltage of the source: $$v = V_m\sin{\omega}t$$
induced emf in the inductor: $$e = L\frac{di}{dt}$$

The Attempt at a Solution

By Kirchhoff's second rule, v - e = 0. What puzzles me is that this would basically mean that there's no current going through the circuit, wouldn't it? But then there would be no induced emf in the inductor, so that's probably not the case. How come there's some current going through the circuit when the induced emf opposes the source emf?

the fact that $V_{source} - V_{inductor} = 0$ does not imply that there is no current! (think of a simple DC circuit with a single resistor...there again th esum of the potential differences is zero and yet there is a current).

Quite the opposite, for $V_{inductor}$ to be nonzero the current must be changing in time.

So you have to solve the differential equation. But the fastest way to answer the question is to simply use that the impendance of an inductor is given by $\omega L$ and then the current is the voltage of the source divided by the impedance (and is out of phase by 90 degrees)

 

[m2003]

In an AC circuit with an inductor, the current is not constant and is instead changing over time. This is because the inductor resists changes in current, leading to a lag between the applied voltage and the resulting current. In this case, the induced emf in the inductor does oppose the source emf, but this does not mean that there is no current in the circuit. The current will still flow, but it will be lower than the current that would flow in a purely resistive circuit with the same voltage source. This is due to the inductive reactance, which is the opposition to current flow caused by the inductor. To determine the current in this circuit, you can use the equation I = V/R, where V is the voltage of the source and R is the total resistance in the circuit, including the inductive reactance. This will give you the peak current in the circuit, which will vary over time as the voltage changes.