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3.9 Inductance Behavior

Except for some transient moments, when we directly apply direct current to a coil is similar to a resistor having a resistance equals to its own internal resistance. A circuit containing a switch, a coil, and a voltage source is a R-L circuit (Fig. 3.21).

A simple circuit diagram showing a DC voltage source labeled "Vdc" connected in series with a switch, a resistor labeled "R," and an inductor labeled "L." The circuit forms a closed loop.

Fig. 3.21 Inductive R-L circuit. Source Own elaboration

Let us now examine the transient behavior of an inductor in a DC circuit. This will give us an insight of how alternating current circuits operate.

Recalling $e = \frac{d Φ}{d t}$ , Where Φ represents magnetic flux and "e" denotes the emf generated (lower case because is a variable magnitude). This is how we explain the relationship between the two:

$Φ = L \cdot i$ (3.22)

We have:

$d Φ = L d i$ (3.23)

Since L is constant. The result is:

$e = - L \cdot \frac{d i}{d t}$ (3.24)

Upon closing, a self-induced current appears which opposes the flow of current that generates it.

练习题

When a direct current is applied to a coil and all transient effects have subsided, how does the coil behave?

A. It behaves as an open circuit with infinite resistance

B. It behaves like a resistor with resistance equal to its internal resistance

C. It behaves like a capacitor storing charge

D. It behaves as a short circuit with zero resistance

Which of the following components are required to form an R-L circuit as described in the text?

A. A switch

B. A capacitor

C. A coil (inductor)

D. A voltage source

E. A resistor (explicit or internal)

The induced electromotive force (emf) in an inductor is directly proportional to the magnitude of the magnetic flux passing through it.

The magnetic flux through an inductor is proportional to the current flowing through it, as expressed by $Φ = L \cdot i$ .

The self-induced electromotive force in an inductor is given by the equation $e = ___ \cdot \frac{di}{dt}$ , where the negative sign indicates that the induced emf opposes the change in current.

When a switch in an R-L circuit is closed, what happens to the self-induced current in the coil?

A. It flows in the same direction as the applied current, enhancing it

B. It opposes the flow of current that generates it

C. It remains zero until the magnetic field stabilizes

D. It instantly reaches its maximum value

Why is it useful to examine the transient behavior of an inductor in a DC circuit?

The equation $d Φ = L d i$ is valid because inductance L is assumed to be constant.

Which of the following statements correctly describe similarities or differences between capacitors and inductors?

A. Both capacitors and inductors are passive circuit elements that can store energy

B. Capacitors store energy in an electric field, while inductors store energy in a magnetic field

C. Both elements exhibit transient behavior when connected to DC sources

D. A capacitor's voltage cannot change instantaneously, while an inductor's current cannot change instantaneously

E. Neither element can ever behave like a resistor

Starting from $Φ = L \cdot i$ and $e = \frac{d Φ}{d t}$ , which sequence correctly derives the self-induced emf equation?

Φ = L \cdot i

→

d Φ = L d i

→

e = L \cdot \frac{d i}{d t}

Φ = L \cdot i

→

d Φ = L d i

→

e = - L \cdot \frac{d i}{d t}

Φ = L \cdot i

→

d Φ = \frac{d i}{L}

→

e = - \frac{1}{L} \cdot \frac{d i}{d t}

Φ = L \cdot i

→

d Φ = i d L

→

e = - i \cdot \frac{d L}{d t}

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3.9 Inductance Behavior