Definitions [13]
Whenever there is a change in the number of magnetic field lines linked with a conductor, an electromotive force (e.mf) is developed between the ends of the conductor which lasts as long as there is a change in the number of magnetic field lines through the conductor. This phenomenon is called the electromagnetic induction.
and
Faraday's Definition:
Electromagnetic induction is the phenomenon in which an e.m.f is induced in the coil if there is a change in the magnetic flux linked with the coil.
OR
The phenomenon of producing an induced emf in a conductor or conducting coil due to changing magnetic flux or field is called electromagnetic induction.
Define the coefficient of self-induction.
It is defined as magnetic flux linked with the solenoid when unit current flows through it.
The property of a coil by which it opposes the change in its own current and induces an emf in itself — numerically equal to the ratio of magnetic flux (produced due to current in the circuit) linked with the circuit to the current flowing in it, or the ratio of induced emf produced around the circuit to the rate of change of current in it — is called self-inductance.
Define self-inductance.
The self-inductance of a circuit is the ratio of magnetic flux (produced due to current in the circuit) linked with the circuit to the current flowing in it.
Define mutual inductance.
The mutual inductance (M) of two circuits (or coils) is the magnetic flux (Φs) linked with the secondary circuit per unit current (IP) of the primary circuit.
The property of two coils by which a change in current in one coil induces an emf in the other coil — equal to the magnetic flux linked with one circuit per unit current in the other, or the value of induced emf produced in the secondary circuit per unit rate of change in current in the primary circuit — is called mutual inductance.
Define a Transformer.
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.
An a.c. generator is a device which converts the mechanical energy into the electrical energy using the principle of electromagnetic induction.
When a charged capacitor is allowed to discharge through a non-resistive inductor, electrical oscillations of constant amplitude and frequency are produced; these are called L-C oscillations.
In the expression Pav = VrmsIrms cos ϕ, the quantity cos φ is called the power factor.
Give any one definition of power factor.
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"`
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.
Formulae [4]
Mutual inductance relation (coupling): M = K\[\sqrt {L_1L_2}\]
Pinput = Poutput
P = VI = \[\frac{V_mI_m}{2}[\cos\phi-\cos(2\omega t+\phi)]\]
Pav = VI cos ϕ = I2Z cos ϕ = \[\frac {V_mI_m}{2}\]cos ϕ = VrmsIrms cos ϕ
Theorems and Laws [2]
Two circular loops, one of small radius r and the other of larger radius R, such that R >> r, are placed coaxially with centres coinciding. Obtain the mutual inductance of the arrangement.
Let a current IP flow through the circular loop of radius R. The magnetic induction at the centre of the loop is
BP = `(mu_0I_P)/(2R)`
As, r << R, the magnetic induction BP may be considered to be constant over the entire cross-sectional area of the inner loop of radius r. Hence magnetic flux linked with the smaller loop will be
`Φ_S = B_PA_S = (mu_0I_P)/(2R)pir^2`
Also, ΦS = MIP
∴ M = `Phi_S/I_P = (mu_0pir^2)/(2R)`
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 Pinput = Poutput. On the basis of winding, transformers are of two types — step-up and step-down.
Important Questions [50]
- If ‘R’ is the Radius of Dees and ‘B’ Be the Magnetic Field of Induction in Which Positive Charges (Q) of Mass (M) Escape from the Cyclotron, Then Its Maximum Speed (Vmax) is
- Prove Theoretically Electromagnetic Induction `E = (Dphi)/(Dt)`
- What is electromagnetic induction?
- The Magnetic Induction at a Point Inside the Solenoid Along the Axis
- The Magnetic Flux Through a Loop is Varying According to a Relation Phi = 6t^2 + 7t + 1.Where `Phi` Is In Milliweber and T is in Second. What is the E.M.F. Induced in the Loop at T = 2 Second?
- A Metal Rod Rotates About One of Its Ends Perpendicular to a Plane Whose Magnetic Induction is 4 X 10-3 T.
- The magnetic flux through a loop varies according to the relation Φ = 8t2 + 6t + C, where ‘C’ is constant
- Electric field intensity in free space at a distance ‘r’ outside the charged conducting sphere of radius ‘R’ in terms of surface charge density ‘ a ’ is
- Define the coefficient of self-induction.
- Define self-inductance.
- Explain why the inductance of two coils connected in parallel is less than the inductance of either coil.
- Write the SI Unit and Dimention Of Of Co-efficient of Self Induction
- Explain the Phenomenon of Self Induction.
- The current in a coil changes from 50A to 10A in 0.1 second. The self inductance of the coil is 20H. The induced e.m.f. in the coil is ______.
- The co-efficient of mutual induction between primary and secondary coil is 2H. Calculate induced e.m.f.
- If the Radius of a Sphere is Doubled Without Changing the Charge on It, Then Electric Flux Originating from the Sphere is
- Explain Self Induction and Mutual Induction
- Define Coefficient of Mutual Induction.
- Explain the Phenomenon of Mutual Induction.
- Define mutual inductance.
- An emf of 91 mV is induced in the windings of a coil when the current in o nearby coil is increasing at the rate of 1.3 A/s. what is the mutual inductance (M) of the two coils in mH?
- What is a transformer?
- A circular coil of 100 turns with a cross-sectional area of 1 m2 is kept with its plane perpendicular to the magnetic field of 1 T. The magnetic flux linkage is ______.
- Derive an Expression for Ratio of E.M.F.S and Currents in Terms of Number of Turns in Primary and Secondary Coil.
- Describe the construction and working of a transformer with a neat labelled diagram.
- What is Transformer?
- Distinguish between Step up and Step Down Transformer.
- State the Principle On Which Transformer Works.
- Derive an Expression for E.M.F. and Current in Terms of Turns Ratio
- A Transformer Converts 240 V Ac to 60 V Ac. the Secondary Has 75 Turns. the Number of Turns in Primary Are
- Derive the equation for a transformer.
- Explain the construction and working of the transformer.
- A Coil of 100 Turns, Each of Area 0.02m^2 is Kept in a Uniform Field of Induction 3.5 X10^-5 T.
- Obtain an Expression for the Induced E.M.F. in a Coil Rotating with Uniform Angular Velocity in Uniform Magnetic Field. Plot a Graph of Variation of Induced E.M.F. Against Phase(θ = ωT) Over One Cycle
- Show Graphically the Variation of E.M.F. with Time (T).
- At Which Position of the Plane of the Rotating Coil with the Direction of Magnetic Field, the E.M.F. Induced in the Coil is Maximum ?
- A Capacitor of Capacitance 0.5 μF is Connected to a Source of Alternating E.M.F. of Frequency 100 Hz. What is the Capacitive Reactance? (π = 3.142)
- What is the Inductance of the Coil
- Three Capacitors of Capacities 8 μF, 8 μF and 4 μF Are Connected in a Series and Potential Difference of 120 Volt is Maintained Across the Combination. Calculate the Charge on Capacitor Of Capacity 4 μF.
- Derive an expression for the impedance of an LCR circuit connected to an AC power supply. Draw phasor diagram.
- Discuss the Composition of Two S.H.M.S Along the Same Path Having Same Period. Find the Resultant Amplitude and Intial Phase.
- Six capacitors of capacities 5, 5. 5, 5, 10 and X μ F are connected as shown in the network in the diagram
- If A.C. Voltage is Applied to a Pure Capacitor, Then Voltage Across the Capacitor
- A Solenoid 3.142m Long and 5.0 Cm in Diameter Has Two Layers of Windings of 500 Turns Each and Carries a Current of 5a. Calculate the Magnetic Induction at Its Centre Along the Axis.
- Calculate Total Normal Electric Induction Over the Closed Surface.
- In Series Lcr Circuit at Resonance, Phase Difference Between Current and E.M.F. of Source is
- An A.C. Circuit Consists of Inductor of Inductance 125 Mh Connected in Parallel with a Capacitor of Capacity 50 μF. Determine the Resonant Frequency.
- Obtain an expression for average power dissipated in a purely resistive A.C. circult.
- What is the average value of alternating current over a complete cycle?
- In a series LCR circuit, the phase difference between the voltage and the current is 45°. Then the power factor will be ______.
