Electromagnetic Induction Flashcards
Define magnetic flux
The total number of magnetic field lines passing normally through a given area is known as magnetic flux through that area.
Define electromagnetic induction
The phenomenon of producing induced emf or current in a conductor or coil due to change in magnetic flux or field is called electromagnetic induction.
Expression for magnetic flux through a given area
d(phi) = Bcos(theta).ds
SI unit of magnetic flux
Wb
SI unit of magnetic induction
Wb/(m*m) or T
State Faraday’s first law of electromagnetic induction
Faraday’s first law states that whenever there is a change in flux associated with the coil, an emf is induced in the coil.
State Faraday’s second law of electromagnetic induction
According to Faraday’s second law of electromagnetic induction, the magnitude of induced emf is directly proportional to the rate of change of magnetic flux through the coil.
State Lenz law of electromagnetic induction
The direction of induced emf or current in the coil or conductor is such as to oppose the change in magnetic flux which produces it.
Explain Faraday’s coil and magnet experiment
Explanation of Lenz law
Pg 257
Tries to oppose change which is responsible for it.
Mechanical energy converted into electrical energy.
In accordance with law of conservation of energy.
Give the theoretical proof of e= -(d(phi)/dt)
Pg 257-258 d(phi)/dt = d(Blx)/dt = Blv f= Bil dW= -Bil.dx dW/dt= ei dw= eidt = -Bildx e=-Blv
State Flemings right hand rule
Stretch the thumb, first finger and middle finger of the right hand so that they are mutually perpendicular to each other. If the first finger represents the direction of magnetic field and the thumb represent the direction of motion of the conductor, then the middle finger represents it direction of induced emf or current in the conductor.
What are Eddy currents?
Every metal consists of a large number of free electrons which are randomly moving within the metal. When the metal is subjected to changing magnetic field or flux, they experience forces and move in circular path of different radii depending in their speeds. There circular paths produce currents which resemble whirlpools or eddies in liquid. Hence, they are called Eddy currents.
How can Eddy currents be demonstrated?
Copper plate suspended by means of thread made to oscillate in its own plane like a pendulum.
Amplitude of oscillations decreases slowly.
If made to oscillate between poles of magnets, oscillations decrease fast and then it stops.
If slots are made amplitude decreases less rapidly.
Why do the oscillations do a copper plate suspended by a long thread, made to oscillate in its own plane like a pendulum stop when it is made to oscillate between the poles of magnet?
Magnetic flux linked with the plate goes on decreasing. Induced currents set up in the copper plate in the form of closed loops. They oppose oscillatory motion and are called Eddy currents.
Why do the oscillations do a copper plate suspended by a long thread, made to oscillate in its own plane like a pendulum stop less slowly when slots are made, when it is made to oscillate between the poles of magnet?
Electrons have to cover larger path to form loops (Eddy currents).
Why are thick blocks of metals never used as core in the transformer? What is used instead?
Eddy currents are set-up. So, generation of heat takes place.
To avoid: cores are made up of thin metal strips insulated from each other known as laminated cores.
Applications of Eddy currents
Deadbeat galvanometer
Induction furnace
Electric brakes
Speedometer
Explain application of Eddy currents in deadbeat galvanometer
Opposes oscillation of coil of insulated wire and brings it quickly to rest position.
Explain application of Eddy currents in Induction furnace
Small piece of metal in rapidly changing electric field. Strong Eddy currents are produced in the block of metal? Large mount of heat is produced and block melts.
Explain application of Eddy currents in electric (magnetic induction) brakes
To stop train, driver cuts off electric power supply to motor.
At the same time magnetic field is applied to the rotating drum fixed to the axle. Strong Eddy currents in rotating drum oppose the motion and train stops almost immediately.
Explain application of Eddy currents in speedometer.
Strong magnet, kept rotating at the speed of the vehicle, in an aluminum drum pivoted by means of a spring.eddy currents produced in drum. Drum turns in direction of magnet. Pointer attached to drum indicated speed on a calibrated scale.
Define self-induction
The phenomenon of production of an induced emf in a coil due to change in current in the same coil is known as self-induction.
What does the self inductance depend on?
Number of turns, shape, area of the coil and also on the material of the core.
What metals increase the value of self-inductance?
Iron, cobalt, nickel
Define self-inductance
The ratio of emf in the coil to the rate of change of current in the same coil is known as self-inductance.
Expression for self-inductance
L= absolute value (e/(di/dt))
Is inductance a scalar or vector quantity?
Scalar
What is the SI unit of Self-inductance?
Henry
What are the dimensions of self-inductance?
[L2 M1 T-2 I-2]
What is an inductance coil or an inductor?
A coil with self-inductance ‘L’ is known as an inductance coil or inductor.
Give reason: self-inductance is also called measure of electrical inertia
Property of the circuit which tries to oppose any change in current in the circuit. Role similar to inertia of a body in mechanics.
What is a choke coil?
It is a coil of large number of turns wound on an insulating cylinder. Plays role of opposition in AC circuit and resistor in DC circuit. It controls current to make discharge uniform.
Give reasons: choke is used in many cases instead of resistor.
If we use resistor instead of choke coil to control alternating current, then wastage of electrical power due to Joules heating is more.
Give reasons: choke coil connected in series in fluorescent tube
To decrease current of AC mains without wasting power. If fluorescent tube is directly connected to AC mains, it will draw a large current and may get damaged.
Define mutual induction
The phenomenon of production of an induced emf in one coil due to change of current in a neighboring coil is known as mutual induction.
Give an expression for mutual induction
M= absolute value(es/(dip/dt))
Define coefficient of mutual induction
Coefficient of mutual induction is defined as the ration of emf induced in one coil to the rate of change of current in the other coil.
What does mutual inductance depend on?
Shape and size of the coils, number of turns, separation between coils, angular orientation between the coils and medium between two coils.
Give the SI unit of mutual inductance
Henry
Give the dimensions of mutual inductance
[L2 M1 T-2 I-2]
What are electromagnetic waves?
Waves of electric and magnetic fields, both varying in time and space and one providing the source of the other.
What is the expression for displacement current?
ε0* (d(φE)/dt)
When is displacement current produced?
Displacement current is produced when electric field or electric flux varies with time.
What is expression for modified Ampere’s circuital law?
Line integral B.dl = (mu0)* (I + ((epsilon0)*(d(phiE)/dt)))
What is the principle of a transformer?
Whenever magnetic flux linked with a coil changes, emf is induced in the neighboring coil.
Construction of a transformer
Two coils- primary and secondary, insulated from each other and wound on a soft-iron core. Primary coil = input coil, secondary coil= output coil.
Derive expression for equation of transformer.
Pg 262 - 263
Give the expression for equation of a transformer.
es/ep = Ns/Np
What is the turns ratio of a transformer?
Ns/Np
Give the relation between turns ratio and current through coils of transformer in case of an ideal transformer
es/ep = Ns/Np = ip/is
What are the two types of transformers?
Step-up : when Ns>Np (es>ep) (isNs (ep>es) (ip<is)
Expression for coil rotating in uniform magnetic induction - derivation
Φ= NABcos(θ) e= -dθ/dt e= 2*π*fsin(ωt)
Give reasons : coil rotating in uniform magnetic induction produces an emf called sinusoidal emf
Emf not constant but varies with time or sin(ωt)
What is the peak value of alternating emf?
Maximum value e0=NABω
What is the relation between emf and frequency in an AC circuit?
Same frequency but phase may or may not differ
Define root mean square current
RMS current is defined as that constant current which produces the same amount (quantity) of heat in a given resistance in a given time as produced by an alternating current, when flowing through the same resistance in the same time.
What is the relation between rms current and peak current?
irms= i0 / root(2)
Relation between root mean square and peak value of AC voltage
erms=e0/root2
Relation between i and e in an AC circuit with resistor
In phase
Relation between i and e for a pure inductor
e leads the current by phase π/2 rad
Or
i lags behind the emf by π/2 rad
Expression for inductive reactance
Xl = ωL = 2πfL = erms/ irms = e0/i0
Define inductive reactance
Inductive reactance can be defined as the ratio of rms voltage across the inductor to the rms current passing through it.
How is the graph of inductive reactance against frequency of the AC source?
Straight line passing through origin.
What is the relation between current and emf in a capacitor?
Emf or voltage across the capacitor lags behind the current by phase π/2 rad or current leads emf or voltage by π/2 rad.
Give the expression for capacitive reactance
Xc= 1/(ωC) = 1/(2πfC) = erms/ irms = e0/i0
Define capacitive reactance
Capacitive reactance is defined as the ratio of rms voltage across the capacitor to the rms current.
Give reasons : capacitor is called blocking capacitor
As f—> 0, Xc—> infinity
So, we can say that capacitor offers infinite resistance to the flow of DC and blocks it. Hence it is called blocking capacitor.
Difference between resistance and reactance of the circuit
- Resistance is the property of the circuit which consumes electric power as heat while a pure inductor and capacitor does not consume any electric power, i.e. No heat is produced.
- Reactance depends on frequency of alternating source while resistance doesn’t.
Mathematical expression for impedance
Z= root((R*R)+(XL-Xc)^2)
Define impedance
Impedance is defined as the ratio of rms voltage to the value of rms current in a LCR circuit.
Give an expression for the phase by which current lags emf in a LCR circuit
tanφ= (eL-ec)/eR = (XL-Xc)/R
Equation for resultant emf and current in an LCR circuit
e= e0sin(ωt+/-φ) i= i0sin(ωt+/-φ)
How are the inductor and capacitor connected for LC oscillations?
Parallel
Explain LC oscillations
Pg 269
Capacitor discharged.
Magnetic field around inductor coil.
Once max magnetic field (capacitor completely discharged), back emf, current flows in the coil, capacitor gets charged with opposite polarity
Power of AC circuit with resistor
Pavg= erms*irms
Power of a series LCR AC circuit
Pavg= ermsirmscosφ
Define power factor
The ratio of true power to apparent power consumed in a circuit is known as power factor.
Expression for power factor of an AC circuit
cosφ = R/Z
Why is current in purely inductive or capacitive AC circuit said to be Wattless?
In purely inductive or capacitive circuit, φ=90deg
So, no average power is consumed in inductor and capacitor.
So, it is said to be Wattless.
When is a circuit said to be Wattless?
When average power consumed in the circuit is zero.
What is idle current?
In a Wattless circuit, current does not do any work, hence it is called idle current.
What is a resonant circuit?
In any AC circuit with inductor and capacitor, when the frequency of AC is gradually changed, at a certain frequency, impedance becomes maximum or minimum. This condition is called resonance and such a circuit is called resonant circuit.
Define resonant frequency for a series LCR circuit
The frequency of AC for which resonance takes place and maximum current (rms) flows through the circuit is called resonant frequency (fr) of a series LCR circuit.
Condition for maximum current (resonance in series LCR circuit)
fr= 1/(2πroot(LC))
Give reasons : Series LCR circuit is called acceptor circuit
Offers high impedance to current many frequencies and minimum impedance to current of resonant frequency. So, it accepts only current of resonant frequency and rejects current of all other frequencies. Hence, it is known as acceptor circuit.
Impedance of a parallel LC AC circuit
Z= 1/(ωC-(1/ωL))
Why is impedance in a parallel LC circuit maximum and not infinite?
Resistance of coil
Define resonant frequency for a parallel LC circuit.
Frequency of AC for which resonance takes place and minimum current flows through the circuit in a parallel LC circuit is known as resonant frequency (fr) for a parallel LR circuit.
Expression for resonant frequency (fr) in a parallel resonance circuit
fr= 1/(2πroot(LC))
Why is zero current not possible practically? (Parallel resonance circuit)
Resistance of the coil
Inductor possesses a small resistance
So at resonant frequency, a small current is drawn from the alternating source.
Why is a parallel resonance circuit called a rejector circuit?
It offers low impedance to currents of other frequencies but offers a very high impedance to current of the resonant frequency. So, it rejects the current of resonant frequency and allows current of other frequencies to pass through it.
Use of series resonance circuit
Radio receivers or TV receivers for tuning the signal from a desired transmitting station or channel.
Use of a parallel resonance circuit
Useful in wireless transmissions or radio communications and filter circuits.
