Electromagnetic Induction and Alternating Current: One Mark Questions, Book Back Answers and Notes

About Electromagnetic Induction and Alternating Current

Hard ~180 min study

In Unit 3 you saw that a current produces a magnetic field. This unit asks the reverse question: can a magnetic field produce a current? Faraday showed that it can, but only when the magnetic flux linked with a circuit changes. Moving a magnet towards a coil, or switching the current in a nearby coil on and off, induces an emf. Power stations, transformers and induction stoves all work on this principle.

The second half of the unit is about alternating current, which changes direction periodically. Resistors, inductors and capacitors each respond to AC in a different way. Phasor diagrams turn these phase relationships into simple vector pictures, so you can see at a glance whether current leads or lags the voltage.

The book back questions here test Lenz's law, eddy currents, transformer efficiency, resonant frequency of an RLC circuit and power factor. You need both the direction rules for induction and careful numerical work with reactance and impedance.

What you'll learn

• Explain how a change in magnetic flux produces an induced emf.
• Use Lenz's law to find the direction of induced current in a given arrangement.
• Calculate self-inductance of a long solenoid and mutual inductance of two coaxial solenoids.
• Derive the mean and RMS values of alternating current.
• Describe the phase relation between voltage and current in R, L and C circuits.
• Solve problems on impedance and resonance in series RLC circuits.
• Identify the energy losses in a transformer and calculate its efficiency.

Before you start

• Magnetic field, field lines and magnetic flux.
• Ohm's law and simple DC circuit analysis.
• Trigonometric functions and vector addition.

Electromagnetic Induction and Alternating Current explained

What This Unit Covers

Faraday's Laws and Lenz's Law

Faraday's first law says an emf is induced whenever the magnetic flux linked with a circuit changes. The second law says the magnitude of the induced emf equals the rate of change of flux linkage. Lenz's law gives the direction: the induced current opposes the change in flux that causes it. This is a consequence of conservation of energy. To push a magnet into a coil against the opposing force, you must do work, and that work appears as electrical energy.

Eddy Currents, Self and Mutual Induction

A changing flux through a solid piece of metal induces circulating currents called eddy currents. They are useful in induction stoves, electromagnetic brakes and dead-beat galvanometers, but they waste energy in transformer cores. Self-induction is the emf induced in a coil by a change in its own current; it opposes that change. Mutual induction is the emf induced in one coil by a changing current in a nearby coil. Transformers work on mutual induction.

AC Generator and Transformer

An AC generator converts mechanical energy into electrical energy by rotating a coil in a magnetic field, so the flux through it changes continuously and gives a sinusoidal emf. A transformer has a primary and a secondary coil wound on a laminated core. It steps AC voltage up or down according to the turns ratio. The losses are copper loss, eddy current loss, hysteresis loss and flux leakage, so no real transformer is 100% efficient. Power is transmitted at high voltage and low current to cut down \( I^2R \) loss in the lines.

Alternating Current and Phasors

A sinusoidal alternating current has a peak value, a mean value over a half cycle and an RMS value. The RMS value is the steady direct current that produces the same heating in a resistor, and for sinusoidal AC \( I_{rms} = \frac{I_0}{\sqrt{2}} \). The mean over a full cycle is zero, which is why the half cycle is used. Phasors are rotating vectors that represent these quantities and show phase differences clearly.

AC Circuits with R, L and C

In a pure resistor, voltage and current are in phase. In a pure inductor, current lags voltage by \( \frac{\pi}{2} \). In a pure capacitor, current leads voltage by \( \frac{\pi}{2} \). Inductive reactance \( X_L = \omega L \) increases with frequency, while capacitive reactance \( X_C = \frac{1}{\omega C} \) decreases with frequency. Resistance does not depend on frequency.

Series RLC Circuit and Resonance

In a series RLC circuit, the impedance is \( Z = \sqrt{R^2 + (X_L - X_C)^2} \). At the resonant frequency, \( X_L = X_C \), the impedance is minimum and equal to R, and the current is maximum. Series resonance is used in the tuning circuit of a radio receiver to pick one station out of many.

Power in AC Circuits

Average power in an AC circuit is \( P = V_{rms} I_{rms} \cos\phi \), where \( \cos\phi \) is the power factor. Only the resistor uses up energy; an ideal inductor or capacitor stores energy for part of the cycle and returns it. A pure inductor or capacitor has a power factor of zero, and the current through it is called wattless current. A power factor close to one delivers the most power for a given current.

Common mistakes to avoid

• Confusing magnetic flux (in weber) with magnetic flux density (in tesla). Induced emf depends on the rate of change of flux, \( \Phi = BA\cos\theta \).
• Using Fleming's left hand rule for induced current. For the direction of induced current in a moving conductor, use Fleming's right hand rule.
• Assuming the mean value of AC over a full cycle gives its heating effect. The full cycle mean is zero; heating depends on the RMS value.
• Treating reactance as a fixed number. \( X_L \) rises and \( X_C \) falls as frequency increases.
• Adding R and X directly to get impedance. They are 90 degrees apart, so use \( Z = \sqrt{R^2 + (X_L - X_C)^2} \).

Test yourself on these with the practice test, then check the worked reasoning in the solved MCQs.

Frequently asked questions

How does Lenz's law follow from conservation of energy?

Suppose the induced current helped the change instead of opposing it. A magnet pushed slightly towards a coil would then be pulled in faster, producing more current with no work done, which would create energy from nothing. Because the induced current opposes the motion, you must do work to move the magnet, and that work is what becomes electrical energy.

What are eddy currents and how are they reduced?

Eddy currents are loops of current induced inside a bulk conductor when the flux through it changes. They heat the conductor and waste energy. In transformer cores they are reduced by using thin laminated sheets insulated from each other, which breaks up the large current loops.

How does an inductor differ from a resistor in an AC circuit?

A resistor turns electrical energy into heat and keeps current in phase with voltage. An ideal inductor stores energy in its magnetic field and gives it back, and the current lags the voltage by 90 degrees. Averaged over a full cycle, an ideal inductor consumes no power.

Why do we use the RMS value of alternating current?

The RMS value is the direct current that would produce the same heat in the same resistor in the same time. It lets you use the DC formulas for power with AC. The 230 V of household supply in India is an RMS value; the peak value is about 325 V.

Why is resonance used in radio receivers?

At resonance the current in a series RLC circuit is maximum for one particular frequency. By changing the capacitance of the tuning circuit, the resonant frequency is matched to the frequency of the station you want, so that station's signal is picked up strongly and others are weak.

How does a transformer change voltage without moving parts?

Alternating current in the primary coil produces a changing magnetic flux in the core. The same flux links the secondary coil and induces an emf in it. For an ideal transformer, the ratio of secondary to primary voltage equals the ratio of the number of turns in the secondary to that in the primary.