Revision: Electromagnetic Induction and Alternating Current Physics HSC Science Class 12 Tamil Nadu Board of Secondary Education

Electromagnetic induction is the production of an electromotive force across an electrical conductor in a changing magnetic flux or magnetic field.

The total number of magnetic field lines passing perpendicularly through a given surface area.

The circulating currents induced in conductive materials (bulk pieces of conductors) when the magnetic flux linked with them changes, due to exposure to changing magnetic fields, are called eddy currents.

An a.c. generator is a device which converts the mechanical energy into the electrical energy using the principle of electromagnetic induction.

The transformer is a device used for converting low voltage into high voltage and high voltage into low voltage. It works on the principle of electromagnetic induction.

An electrical device which converts low alternating voltage at high current to high alternating voltage at low current (or vice versa) — i.e., a device which reduces or increases the voltage in an AC circuit through mutual induction — is called a transformer.

The Power Factor is the ratio of True Power (measured in Watts) to Apparent Power (measured in Volt-Amperes) in an AC circuit.

Power factor (cos Φ) = `"True power"/"Apparent power"`

In the expression Pav = V_rmsI_rms cos⁡ ϕ, the quantity cos φ is called the power factor.

OR

Power Factor is the cosine of the phase angle (φ) between the voltage and current in an AC circuit. It equals the ratio of true (average) power to apparent power.

The current flowing in a purely inductive or purely capacitive circuit for which cos φ = 0 and no power is dissipated even though the current is flowing is called wattless current.

OR

Wattless Current (also called reactive current) is the component of current in a purely inductive or purely capacitive circuit that flows without consuming any power.

Φ_B​ = \[\vec B\] ⋅ \[\vec A\] = B A cos θ

Eddy current: i = \[\frac {\text {Induced emf (e)}}{\text {Resistance (R)}}\]

\[\frac{I_p}{I_s}=\frac{N_s}{N_p}=\frac{V_s}{V_p}\]

\[\frac{V_s}{V_p}=\frac{N_s}{N_p}=\frac{I_p}{I_s}=k\]

 P_input = P_output

\[\frac{V_s}{V_p}=\frac{N_s}{N_p}=k\]

Where:

• V_s = Secondary (output) voltage (V)
• V_p = Primary (input) voltage (V)
• N_s = Number of turns in secondary coil
• N_p = Number of turns in primary coil
• k = Transformation ratio (turns ratio)

P = VI = \[\frac{V_mI_m}{2}[\cos\phi-\cos(2\omega t+\phi)]\]

Where:

• V_m​ = Peak voltage
• I_m​ = Peak current
• ϕ = Phase angle between voltage and current
• ω = Angular frequency
• t = Time

\[\cos\phi=\frac{P_{av}}{P_{apparent}}=\frac{P_{av}}{V_{rms}\cdot I_{rms}}\]

P_av ​= VI cos ϕ = I²Z cos ϕ = \[\frac {V_m​I_m}{2}\]​​cos ϕ = V_rms​I_rms​ cos ϕ

Faraday's First Law

Whenever the magnetic flux linked with a circuit changes, an EMF is induced in the circuit. The induced EMF lasts only as long as the change in flux is taking place.

Faraday's Second Law

The magnitude of the induced EMF in a circuit is directly proportional to the rate of change of magnetic flux through the surface enclosed by that circuit.

A transformer is based on the principle of mutual induction, i.e., whenever the magnetic flux linked with a coil changes, an emf is induced in the neighbouring coil. For an ideal transformer there is no loss of power, so P_input = P_output​. On the basis of winding, transformers are of two types — step-up and step-down.

• Electromagnetic induction requires a changing magnetic flux — a static field produces no induction
• The faster the change in flux, the greater the induced EMF (Faraday's Second Law)
• The induced EMF exists only during the change; it ceases when the flux becomes constant
• Both the motion of a conductor in a magnetic field and the change of current in a nearby circuit can cause induction
• The direction of the induced current can be found using Fleming's Right-Hand Rule or Lenz's Law