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Chapter 29: Problem 7

Which of the following statements regarding self induction is correct? a) Self-induction occurs only when a direct current is flowing through a circuit. b) Self-induction occurs only when an alternating current is flowing through a circuit. c) Self-induction occurs when either a direct current or an alternating current is flowing through a circuit. d) Self-induction occurs when either a direct current or an alternating current is flowing through a circuit as long as the current is varying.

Short Answer

Expert verified
Answer: Self-induction occurs when either a direct current or an alternating current is flowing through a circuit as long as the current is varying.

Step by step solution

01

Analyze each option

Let's analyze each statement given: a) Self-induction occurs only when a direct current is flowing through a circuit. b) Self-induction occurs only when an alternating current is flowing through a circuit. c) Self-induction occurs when either a direct current or an alternating current is flowing through a circuit. d) Self-induction occurs when either a direct current or an alternating current is flowing through a circuit as long as the current is varying.
02

Understand self-induction

Self-induction occurs when a changing current in a coil creates a varying magnetic field, which in turn induces an electromotive force (EMF) in the same coil. This induced EMF opposes the change in the original current, according to Lenz's law.
03

Evaluate statement a

In a direct current (DC) circuit, the current does not change and remains constant. Since self-induction requires a change in current to induce an EMF, it is incorrect to say that self-induction occurs only when a direct current is flowing. We can eliminate option a.
04

Evaluate statement b

In an alternating current (AC) circuit, the current constantly changes direction. The changing current creates a varying magnetic field, leading to self-induction. This statement is partially true, but we need to evaluate the other options to make sure there isn't a more correct statement.
05

Evaluate statement c

As discussed in steps 3 and 4, self-induction does occur with an alternating current. However, in direct current circuits, self-induction can also occur when there is a change in the current, such as when a switch is opened or closed. Therefore, it is correct to say that self-induction occurs when either a direct current or an alternating current is flowing, but it is not accurate to say it occurs all the time with direct current.
06

Evaluate statement d

This statement explains that self-induction occurs in both direct current and alternating current circuits, as long as there is a change or variation in the current. This is a more accurate and complete description of the conditions under which self-induction occurs, and makes it the best answer among the given options.
07

Choose the correct statement

Based on the analysis of each statement, we can conclude that the correct statement regarding self-induction is option d: Self-induction occurs when either a direct current or an alternating current is flowing through a circuit as long as the current is varying.

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Most popular questions from this chapter

An 8 -turn coil has square loops measuring \(0.200 \mathrm{~m}\) along a side and a resistance of \(3.00 \Omega\). It is placed in a magnetic field that makes an angle of \(40.0^{\circ}\) with the plane of each loop. The magnitude of this field varies with time according to \(B=1.50 t^{3}\), where \(t\) is measured in seconds and \(B\) in teslas. What is the induced current in the coil at \(t=2.00 \mathrm{~s} ?\)

A square conducting loop with sides of length \(L\) is rotating at a constant angular speed, \(\omega\), in a uniform magnetic field of magnitude \(B\). At time \(t=0\), the loop is oriented so that the direction normal to the loop is aligned with the magnetic field. Find an expression for the potential difference induced in the loop as a function of time.

Your friend decides to produce electrical power by turning a coil of \(1.00 \cdot 10^{5}\) circular loops of wire around an axis parallel to a diameter in the Earth's magnetic field, which has a local magnitude of \(0.300 \mathrm{G}\). The loops have a radius of \(25.0 \mathrm{~cm} .\) a) If your friend turns the coil at a frequency of \(150.0 \mathrm{~Hz}\) what peak current will flow in a resistor, \(R=1500 . \Omega\) connected to the coil? b) The average current flowing in the coil will be 0.7071 times the peak current. What will be the average power obtained from this device?

A wire of length \(\ell=10.0 \mathrm{~cm}\) is moving with constant velocity in the \(x y\) -plane; the wire is parallel to the \(y\) -axis and moving along the \(x\) -axis. If a magnetic field of magnitude \(1.00 \mathrm{~T}\) is pointing along the positive \(z\) -axis, what must the velocity of the wire be in order to induce a potential difference of \(2.00 \mathrm{~V}\) across it?

Which of the following will induce a current in a loop of wire in a uniform magnetic field? a) decreasing the strength of the field b) rotating the loop about an axis parallel to the field c) moving the loop within the field d) all of the above e) none of the above
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