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Basic Electricity & Magnetism Atoms are made up of electrons and protons Electrons are negatively charged particles Protons are positively charged particles Protons and Electrons exert force on one another This additional force is attributed to the charge carried by them, hence protons repel protons, but get attracted to electrons and electrons repel each other. If you have a wire and maintain a charge difference across it – then there will be a charge flow, and the wire carrying the charge is said to be an electric circuit. Electric Circuit An electric circuit is one in which charged particles can move. It is a pipeline that facilitates the transfer of charged particles from one point to another. What it requires is a difference in charge across its two points. The total amount of charge at any point is measured in Coulomb. This difference in charge is called the voltage across the two points. Hence defining Voltage It is the difference in potential or charge across two points and is measured in volts. When there is a charge flow across the two end-points – there is a related rate of charge flow – which is defined by the current in the wire. Hence defining Current It is the change in electric charge with respect to time and is measured in ‘amperes’ Q1 – Q2 / time amperes I = q/ t - change in charge / change in time When there are two points maintained one having a more positive charge than the other, then the electrons will start flowing towards the positively charged point. Current flow is measured as It is the flow of negatively charged particles (electrons) towards the positive terminal hence it is –I amperes or It is the flow of positively charged particles (holes) towards the negative terminal hence it is +I amperes. Current types If you maintain a constant voltage difference between two points – you get a Direct current: eg batteries – voltage does not change with the time But if the voltage keeps varying – you will get an alternating current. Alternating current- eg household power, oscillates between positive and negative volts with a given frequency Usage of voltage - you want it to flow across some component – so you attach the component through which you want a current flow across a battery of AC points. This component offers a resistance to the current flow and typically the electric circuit for this is as shown below V I Resistance Basic DC circuit battery According to Ohm – after which the resistance measurement was named If V = 10volts, R = 20 ohms, then V = IR , I = V/R= 10/20 = 0.5 A Power is given by = VI= 10 * 0.5 = 5 watts Ohm’s Law Voltage across a resistance is directly proportional to the current flowing through it Resistive circuits with time varying voltages V(t) = R* I(t), where R is in ohms P =VI = V2/R = I2R Under varying voltages some components are there which exhibit different behavior than the resistance – one example of such a component is the ‘capacitor’ Capacitance (measured in farads) A capacitor has 2 conductive surfaces separated by a dielectric material. A dielectric material prevents flow of direct current and is able to hold the electrostatic charge across the two surfaces. It allows alternating current to go through. The amount of alternating current it allows depended on its capacitance and other components in the circuit. Hence it is used very often to block DC component of current Used to selectively bypass or filter some selected AC components by proper values of capacitance and other components. They can be used for filtering, coupling or bypassing Stray capacitance is present anytime there is a difference in potential between 2 conducting material separated by a dielectric. Creates unwanted capacitive actions Capacitance = Total charge in coulombs / Voltage = Q/V Q = CV dQ/dt = C dv(t) /dt i(t) = C dv(t) /dt Another effect felt in Alternating current is the inductive effect. Inductance (measured in henry’s) It is the property of an electric circuit, by which if there is a changing magnetic field, then associated with it is an electromotive force or voltage. Hence if there is a conducting wire in the form of a coil, through which there is an alternating current flowing, associated with it is a magnetic field and an inductance or inductive effect. V(t) = L di(t)/dt 1H = 1 volt sec/ampere Basic AC circuit Frequency = cycle / sec Resistor V V I capacitor cycle Inductor Ohms law for AC circuits As AC circuits can have different types of components besides resistance – generally Impedance (Z) replaces R V = IZ Z = R + XL + XC f is the frequency of the alternating current. The inductance and capacitor have impedance only when al AC current flows through. If the frequency of the alternating current is f then XL = 2fL Xc = 1/ 2fC Conductance (measured in siemens) G = 1/R 1 Siemen = 1A/V i(t) = G v(t) Magnetism DC current results in a stable magnetic field AC current results in a fluctuating (expanding and collapsing) magnetic field Example Stable magnetic field – around a magnet Fluctuating magnetic field around a wire carrying AC current Magnetic field A bar magnet has magnetic field – lines of magnetic force called magnetic flux around them. The magnetic lines flow form north to south pole Fig 1. N N S S Bend the bar magnet to form a horse shoe – magnetic lines flow across the poles as shown When a current flows through a conductor there are magnetic lines are around this conductor. If the current flow is increased – there will be an increase in the magnetic field Fig 2. wire Direction of current Direction of magnetic field Right hand rule – this rule gives the relationship between current and direction of force. Hold the conductor with right hand with thumb pointing in the direction of current flow. The fingers curls in the direction of the magnetic field Twist the conductor into a coil. The coil will have current flowing if it is cutting a magnetic field. Generators use magnetic force to generate electricity. Mechanical movement is required to move a coil of wire in a magnetic field thereby cutting the magnetic field and voltage develops at the ends of wires Motors use magnetic force to obtain mechanical motion from electrical input, in a similar way to the generators Inducing a current When a conductor cuts through lines of magnetic force – it induces an electromotive force emf or voltage. The magnetic field or conductor should be moving for this to happen i.e. to cut the magnetic lines. If the direction in which the magnetic field is cut changes then direction of emf changes Faraday’s law – states that induced voltage can be determined by the number of turns in a coil and how fast the coil cuts through the magnetic field. Stronger the magnetic field more the current. More turns in the coil – more current When coil turns in half a circle, current flows in one direction, if coil turns the other half circle in a magnetic field, then current is induced in another direction (changed polarity). This produces alternating current. Fig 3. S N 1 S N S N S N 2 1 2 S N 2 2 1 1 1 To produce DC current – a commutator is required. A commutator, switches voltage pick up points to produce current flow in one direction. Hence a commutator converts AC current to DC current. DC generators A device that turns rotary motion to electrical energy – DC current in this case. Brushes are used as electrical pickup points. For one half cycle, the brushes are making contact with either commutator rings (split). For the next half cycle, when a reverse current is flowing through the coil, the brushes are making contact with the opposite commutator rings, thereby making the current flow in one direction. DC current motors Motors convert electrical energy into mechanical energy. The flow of DC current through the coil in a magnetic field makes the coil move. This is the principle behind the DC motors. 2 http://microscopy.fsu.edu/electromag/electricity/generators/