Chapter 21 Magnetic Induction and Chapter 22.9: Transformers

Magnetic Induction Faraday’s Law Lenz’s Law “A changing magnetic flux induces an electromotive force (emf)” Lenz’s Law “the magnetic field produced by an induced current always opposes any changes in the magnetic flux”

Example: Falling Magnet Suppose a bar magnet falls downward through a loop of wire, north pole first. What is the direction of the induced current? Suppose a bar magnet falls upward through a loop of wire, south pole first. N v S v

Inductance Consider the circuit shown When the switch is closed Current flows through the solenoid and produces a magnetic field The magnetic field changes the flux through the solenoid The changing flux induces an emf to oppose the change in flux

Inductance, cont. Induced emf acts like a battery pushing current in the opposite direction This phenomenon is called self-inductance (or inductance) The current changing through a coil induces a current in the same coil The induced current opposes the original applied current, from Lenz’s Law Section 21.4

Inductance of a Solenoid Faraday’s law can be used to find the inductance of a solenoid L is the symbol for inductance The unit of inductance is the henry 1 H = 1 V . s / A The voltage across the solenoid can be expressed in terms of inductance Section 21.4

Inductor The principle applies to all coils or loops of wire The value of L depends on the physical size and shape of the circuit element The circuit element that uses self-inductance is called an inductor Section 21.4

Inductor, cont. The voltage drop across an inductor is Whenever the current through an inductor changes, a voltage is induced in the inductor that opposes this change Many inductors are constructed as small solenoids Almost any coil or loop will act as an inductor Section 21.4

Real Inductors Most practical inductors are made by wrapping a wire coil around a magnetic material The magnetic material increases the inductance Magnetic material has greater permeability than free space Most inductors contain a material that produces a larger L in a smaller package Section 21.5

RL Circuit Combined with capacitors, they form RLC Circuits An RL Circuit is a circuit composed of any number of resistors, inductors, and voltage sources Combined with capacitors, they form RLC Circuits RLC circuits can describe almost any electronic circuit RLC circuits are discussed in Chapter 22 Section 21.5

RL Circuit, cont. Before switch is closed, No current flows (open circuit) so I = 0 No current suggests no potential difference across circuit components VR = 0 VL = 0 Section 21.5

RL Circuit, cont. When switch is closed (t = 0), Inductor keeps current at same value it was before so I = 0 No current in the resistor means no potential difference across the resistor VR = 0 Kirchhoff’s loop rule indicates VL = V Section 21.5

RL Circuit, cont. After a long time (t = ∞), Back emf from inductor decreases until there is no change in the current VL = 0 Kirchhoff’s loop rule indicates VR = V All the voltage change is across the resistor I = V / R Section 21.5

RL Circuit, cont. Because the inductor opposes any change in current, a similar phenomenon occurs when the switch is opened Section 21.5

Time Constant for RL Circuit The current at time t is found by For a single resistor in series with a single inductor, The voltage is given by VL = V e-t/τ Section 21.5

Energy in an Inductor Energy is stored in the magnetic field of an inductor The energy stored in an inductor is Very similar in form to the energy stored in the electric field of a capacitor The expression for energy stored in a solenoid is Section 21.6

Magnetic Energy Density Energy contained in the magnetic field actually exists anywhere there is a magnetic field, not just in a solenoid Can exist in “empty” space The potential energy can also be expressed in terms of the energy density in the magnetic field This expression is similar to the energy density contained in an electric field Section 21.6

Induction Puzzle Consider a very long solenoid is inserted at the center of a single loop of wire The field from the solenoid at the outer loop is essentially zero Resolution leads to electromagnetic waves (Chapter 23) Section 21.8

Mutual Inductance It is possible for the magnetic field of one coil to produce an induced current in a second coil The coils are connected indirectly through the magnetic flux The effect is called mutual inductance Section 21.4

Transformers Transformers make use of mutual inductance to increase or decrease the amplitude of an applied AC voltage A simple transformer consists of two solenoid coils with the loops arranged so that all or most of the magnetic field lines and flux generated by one coil pass through the other coil Section 22.9

Transformers, cont. The wires are covered with a nonconducting layer so that current cannot flow directly from one coil to the other An AC current in one coil will induce an AC voltage across the other coil An AC voltage source is typically attached to one of the coils called the input coil The other coil is called the output coil

Transformers, Equations Faraday’s Law applies to both coils If the input coil has Nin coils and the output coil has Nout turns, the flux in the coils is related by The voltages are related by Section 22.9

Transformers, final The ratio of the turns can be greater than or less than one Therefore, the input voltage can be transformed to a different value Transformers cannot change DC voltages Since they are based on Faraday’s Law Section 22.9

Practical Transformers Most practical transformers have central regions filled with a magnetic material This produces a larger flux, resulting in a larger voltage at both the input and output coils The ratio Vout / Vin is not affected by the presence of the magnetic material Section 22.9

Transformers and Power The output voltage of a transformer can be made much larger by arranging the number of coils According to the principle of conservation of energy, the energy delivered through the input coil must either be stored in the transformer’s magnetic field or transferred to the output circuit Over many cycles, the stored energy is constant The power delivered to the input coil must equal the output power Section 22.9

Power, cont. P = V I Pin = Pout only in an ideal transformer if Vout > Vin, then Iout < Iin Pin = Pout only in an ideal transformer In real transformers, the coils always have a small electrical resistance which causes some power dissipation For a real transformer, the output power is always less than the input power (usually by only a small amount) Small current means little power loss to resistance of power lines Section 22.9

Applications of Transformers Transformers are used in the transmission of electric power over long distances Power dissipation in a electrical wire is P = V I DC voltage would waste too much energy in transmission Transformers allow large AC voltage transmission with small current Many household appliances use transformers to convert the AC voltage at a wall socket to the smaller DC voltages needed in many devices Section 22.9

Applications of Induction A ground fault interrupter (GFI) is a safety device used in many household circuits It uses Faraday’s Law along with an electromechanical relay The relay uses the current through a coil to exert a force on a magnetic metal bar in a switch During normal operation, there is zero magnetic field in the relay If the current in the return coil is smaller, a non-zero magnetic field opens the relay switch and the current turns off Section 21.7

Electric Guitars An electric guitar uses Faraday’s Law to sense the motion of the strings The string passes near a pickup coil wound around a permanent magnet As the string vibrates, it produces a changing magnetic flux The resulting emf is sent to an amplifier and the signal can be played through speakers Section 21.7

Railgun Current produces a large magnetic field which interacts with the current to produce a large force on the projectile Projectile speeds much greater than conventional ballistics are possible Proposed uses are Weapons Space Program Inertial Confinement Fusion http://www.youtube.com/watch?v=6BfU-wMwL2U