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

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. Answer: 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.

Step-by-step solution

Understand self-induction

Self-induction is the phenomenon where a changing current through a coil (conductor) creates a changing magnetic field, which in turn induces an electromotive force (EMF) in the coil itself. This process is based on Faraday's Law of Electromagnetic Induction. Step 2: Analyze statement (a)

Analyze statement (a)

Statement (a) states: "Self-induction occurs only when a direct current is flowing through a circuit." A direct current is a constant current, so there is no change in the magnetic field, and therefore, self-induction will not occur. Step 3: Analyze statement (b)

Analyze statement (b)

Statement (b) states: "Self-induction occurs only when an alternating current is flowing through a circuit." An alternating current is a constantly changing current, causing a change in the magnetic field, which leads to self-induction. So, self-induction occurs in the case of alternating current. Step 4: Analyze statement (c)

Analyze statement (c)

Statement (c) states: "Self-induction occurs when either a direct current or an alternating current is flowing through a circuit." As we have already seen, self-induction does not occur with direct current, so this statement is incorrect. Step 5: Analyze statement (d)

Analyze statement (d)

Statement (d) states: "Self-induction occurs when either a direct current or an alternating current is flowing through a circuit as long as the current is varying." This statement means that self-induction occurs when the current is changing, regardless of whether it is AC or a varying DC. Since we know from Step 3 that self-induction occurs with varying AC, this statement is also correct. Step 6: Conclusion

Conclusion

Based on the analysis in the previous steps, the correct answer is statement (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 one of the pivotal concepts in understanding how many electrical devices work. Imagine you have a coil of wire near a magnet. As per the wonders of physics, if you move the magnet around or change the magnetic field strength, you can actually create or 'induce' an electric current in the wire. This is the fundamental principle behind generators, transformers, and even the charging of your electric toothbrush.

The magic happens because the magnetic field, when changing over time, exerts a force on the electric charges in the wire, setting them in motion. This process is used in a huge variety of applications, from generating power in power plants to the functioning of the induction stovetops in many kitchens.

Faraday's Law

Moving on to Faraday's Law, let's break this down into a simple thought experiment. If you wiggle a magnet near a loop of wire, you induce an electromotive force (EMF) in that wire. Faraday's Law quantitatively relates this induced EMF to the rate of change of the magnetic flux.

In mathematical terms, Faraday's Law is expressed as \( EMF = -N \frac{d\Phi_B}{dt} \), where \(EMF\) is the induced electromotive force, \(N\) is the number of turns of the coil, and \(d\Phi_B/dt\) represents the rate of change of the magnetic flux through one loop. The negative sign, as explained by Lenz's Law, indicates that the induced EMF creates a current whose magnetic field opposes the change in the original magnetic field—nature’s way of saying 'I don’t like change'.

Alternating Current

As our lives oscillate between work and home, so does alternating current, or AC, oscillate in direction and magnitude in our power lines. AC is like a dance of electrons that changes direction and intensity at a regular interval. This is perfect for our power systems because it can easily transform into different voltages using transformers.

Home outlets typically provide AC, which makes it easy to adjust voltage to suit the needs of everything from your laptop to your refrigerator. Industrial applications benefit from this feature of AC, making it the backbone of power distribution systems. Moreover, AC facilitates the induction principle to work in motors and generators, which convert electrical energy into mechanical energy and vice versa, propelling the modern world’s machinery.

Direct Current

Direct Current (DC), unlike its hyper cousin AC, is the steadfast flow of electric charge in one unchanging direction. Found in everything from the batteries that power your remote control to the solar panels on your roof, DC is essential for gadgets and devices that need a constant and steady voltage.

While DC may not be as easily transformed into different voltages like AC, it is perfect for low-voltage or battery-powered devices. And interestingly enough, in the world of high-voltage power transmission, DC is making a comeback with HVDC (high-voltage direct current) systems being used to efficiently transmit power over long distances without the losses associated with AC systems.