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**Electromagnetic Induction**

emf is induced in a conductor placed in a magnetic field whenever there is a change in magnetic field.

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**Moving Conductor in a Magnetic Field**

Consider a straight conductor moving with a uniform velocity, v, in a stationary magnetic field. The free charges in the conductor experience a force which will push them to one end of the conductor. An electric field is built up due to the electron accumulation. An e.m.f. is generated across the conductor such that E = Blv.

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**Induced Current in Wire Loop**

An induced current passes around the circuit when the rod is moved along the rail. The induced current in the rod causes a force F = IlB, which opposes the motion. Work done by the applied force to keep the rod moving is Electrical energy is produced from the work done such that E = E It = W E = Blv

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Lenz’s Law The direction of the induced current is always so as to oppose the change which causes the current.

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Magnetic Flux The magnetic flux is a measure of the number of magnetic field lines linking a surface of cross-sectional area A. The magnetic flux through a small surface is the product of the magnetic flux density normal to the surface and the area of the surface. Unit : weber (Wb)

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**Faraday’s Law of Electromagnetic Induction**

The induced e.m.f. in a circuit is equal to the rate of change of magnetic flux linkage through the circuit. The ‘-’ sign indicates that the induced e.m.f. acts to oppose the change.

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**Induced Currents Caused by Changes in Magnetic Flux**

The magnetic flux (number of field lines passing through the coil) changes as the magnet moves towards or away from the coil.

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Faraday Disk Dynamo

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Simple a.c. Generator According to the Faraday’s law of electromagnetic induction,

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Simple d.c. Generator

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Eddy Current An eddy current is a swirling current set up in a conductor in response to a changing magnetic field. Production of eddy currents in a rotating wheel

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**Applications of Eddy Current (1)**

Metal Detector

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**Applications of Eddy Current (2)**

Eddy current levitator Smooth braking device Damping of a vibrating system

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Back emf in Motors When an electric motor is running, its armature windings are cutting through the magnetic field of the stator. Thus the motor is acting also as a generator. According to Lenz's Law, the induced voltage in the armature will oppose the applied voltage in the stator. This induced voltage is called back emf.

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**Back emf and Power Multiplying by I, then**

Armature coils, R Driving source, V Back emf, Eb Multiplying by I, then So the mechanical power developed in motor

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**Variation of current as a motor is started**

Larger load Zero load As the coil rotates, the angular speed as well as the back emf increases and the current decreases until the motor reaches a steady state.

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**The need for a starting resistance in a motor**

When the motor is first switched on, =0. The initial current, Io=V/R, very large if R is small. When the motor is running, the back emf increases, so the current decrease to its working value. To prevent the armature burning out under a high starting current, it is placed in series with a rheostat, whose resistance is decreases as the motor gathers speed.

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**Variation of current with the steady angular speed of the coil in a motor**

The maximum speed of the motor occurs when the current in the motor is zero.

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**Variation of output power with the steady angular speed of the coil in a motor**

The output power is maximum when the back emf is ½ V.

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Transformer A transformer is a device for stepping up or down an alternating voltage. For an ideal transformer, (i.e. zero resistance and no flux leakage)

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**Transformer Energy Losses**

Heat Losses Copper losses - Heating effect occurs in the copper coils by the current in them. Eddy current losses - Induced eddy currents flow in the soft iron core due to the flux changes in the metal. Magnetic Losses Hysteresis losses - The core dissipates energy on repeated magnetization. Flux leakage - Some magnetic flux does not pass through the iron core.

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**Designing a transformer to reduce power losses**

Thick copper wire of low resistance is used to reduce the heating effect (I2R). The iron core is laminated, the high resistance between the laminations reduces the eddy currents as well as the heat produced. The core is made of very soft iron, which is very easily magnetized and demagnetized. The core is designed for maximum linkage, common method is to wind the secondary coil on the top of the primary coil and the iron core must always form a closed loop of iron.

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**Transmission of Electrical Energy**

Wires must have a low resistance to reduce power loss. Electrical power must be transmitted at low currents to reduce power loss. To carry the same power at low current we must use a high voltage. To step up to a high voltage at the beginning of a transmission line and to step down to a low voltage again at the end we need transformers.

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**Direct Current Transmission**

Advantages a.c. produces alternating magnetic field which induces current in nearby wires and so reduce transmitted power; this is absent in d.c. It is possible to transmit d.c. at a higher average voltage than a.c. since for d.c., the rms value equals the peak; and breakdown of insulation or of air is determined by the peak voltage. Disadvantage Changing voltage with d.c. is more difficult and expensive.

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Self Induction When a changing current passes through a coil or solenoid, a changing magnetic flux is produced inside the coil, and this in turn induces an emf. This emf opposes the change in flux and is called self-induced emf. The self-induced emf will be against the current if it is increasing. This phenomenon is called self-induction.

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**Definitions of Self-inductance (1)**

Definition used to find L The magnetic flux linkage in a coil the current flowing through the coil. Where L is the constant of proportionality for the coil. L is numerically equal to the flux linkage of a circuit when unit current flows through it. Unit : Wb A-1 or H (henry)

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**Definitions of Self-inductance (2)**

Definition that describes the behaviour of an inductor in a circuit L is numerically equal to the emf induced in the circuit when the current changes at the rate of 1 A in each second.

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Inductors Coils designed to produce large self-induced emfs are called inductors (or chokes). In d.c. circuit, they are used to slow the growth of current. Circuit symbol or

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**Inductance of a Solenoid**

Since the magnetic flux density due to a solenoid is By the Faraday’s law of electromagnetic induction,

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**Energy Stored in an Inductor**

The work done against the back emf in bringing the current from zero to a steady value Io is

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**Current growth in an RL circuit**

At t = 0, the current is zero. So As the current grows, the p.d. across the resistor increases. So the self-induced emf ( - IR) falls; hence the rate of growth of current falls. As t

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**Decay of Current through an Inductor**

Time constant for RL circuit The time constant is the time for current to decrease to 1/e of its original value. The time constant is a measure of how quickly the current grows or decays.

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**emf across contacts at break**

To prevent sparking at the contacts of a switch in an inductive circuit, a capacitor is often connected across the switch. The energy originally stored in the magnetic field of the coil is now stored in the electric field of the capacitor. + -

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Switch Design An example of using a protection diode with a relay coil. + - A blocking diode parallel to the inductive coil is used to reduce the high back emf present across the contacts when the switch opens.

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Non-Inductive Coil To minimize the self-inductance, the coils of resistance boxes are wound so as to set up extremely small magnetic fields. The wire is double-back on itself. Each part of the coil is then travelled by the same current in opposite directions and so the resultant magnetic field is negligible.

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