Question

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

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

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.

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.

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.

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.

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.

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.

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.

Key concepts

Electromagnetic Induction

Electromagnetic induction is a fundamental concept in physics that involves the generation of an electromotive force (EMF) when a magnetic field interacts with a conductor. This effect occurs when there is relative motion between the magnetic field and the conductor, or when the magnetic field itself changes over time. This principle is the basis for the operation of many electrical devices, such as transformers and generators.

The induction process involves several important phenomena:

• Changing Magnetic Fields: Any time a magnetic field changes in strength or direction, it has the potential to induce a voltage in nearby conductive materials.
• Motion-Induced EMF: If a conductor moves through a stationary magnetic field, an EMF is generated within the conductor.
• Lenz's Law: The induced EMF will always act in such a way as to oppose the change in magnetic flux that produced it.

Understanding electromagnetic induction is essential for exploring how electric power is generated and transmitted.

Alternating Current (AC)

Alternating current (AC) is a type of electrical current where the flow of electric charge periodically reverses direction. Unlike direct current (DC), where the current flows in a single direction, AC offers unique advantages, especially in the transmission of electricity over long distances.

One of the key features of AC is its waveform, which is typically sinusoidal. This form allows for efficient energy transfer. Additionally, the ability of AC circuits to easily transform voltages through transformers makes it a preferred choice for powering homes and businesses.

AC is characterized by:

• Frequency: Represented in hertz (Hz), indicating how many times the current changes direction per second.
• Amplitude: The maximum extent of a vibration or oscillation, measured from the position of equilibrium.
• Phase: Describes the relationship between two waveforms traveling through the same space.

AC's versatility is seen in its widespread use across the globe.

Direct Current (DC)

Direct current (DC) refers to the unidirectional flow of electric charge, maintaining a constant polarity. Unlike alternating current (AC), where the current direction changes periodically, DC flows steadily in one direction, making it suitable for certain applications such as battery-powered devices.

DC can be generated through various means, including:

• Batteries: Chemical reactions within the battery produce a steady flow of electricity.
• Rectifiers: Convert AC to DC by allowing current to flow in one direction only.
• Solar Panels: Convert sunlight into DC electricity through photovoltaic cells.

The predictability of DC makes it the power source of choice for electronic circuits, where stability is crucial.
Understanding the differences between AC and DC is critical for selecting the right power source for specific technological needs.

Lenz's Law

Lenz's Law is a principle that helps explain the direction of an induced electromotive force (EMF) and current resulting from a change in magnetic flux. Named after the physicist Heinrich Lenz, this law is rooted in the concept of energy conservation. It states that the direction of the induced EMF will always oppose the change in magnetic flux that caused it.

The law can be summarized through the following ideas:

• Opposition to Change: Any induced current created by changing magnetic fields generates its own magnetic field that opposes the original change.
• Energy Conservation: Ensures that energy within a closed system is neither created nor destroyed, but merely transformed.
• Applications: Lenz's Law is pivotal in understanding how generators, transformers, and induction cooktops work.

This law plays a critical role in electromagnetic theory, highlighting the interconnectedness of electricity and magnetism.