Transcript Document
Electric current DC Circuits AC Circuits Lecture questions Electric current DC Circuits. Ohm's law Resistance and conductance Conductivity of electrolytes Alternating current Resistor, Capacitor and Inductor AC Response Impedance Electric current • An electric current is a directed flow of charged particles. • It may occur when there is a potential difference. • Current, and is the amount of charge flowing through cross section of a conductor per second. q I t dq I qt dt I A Current density I j S A j 2 m Direction • For historical reasons the direction of the current is taken to be the direction of the flow of positive charge. • The flow of positive charge in one direction is equivalent to the flow of negative charge in the opposite direction. Electric current I q0 nvS j q0 nv • q0 charge of each carrier • n - concentration (the number of charge carriers/cubic meter) • v - average speed of charged particles • S - cross sectional area of the conductor Direct current (DC) • DC is the unidirectional flow of electric charge. • Galvanic current is a steady direct electric current. • DC circuit consists of any combination of constant voltage sources, constant current sources, and resistors. In this case, the circuit voltages and currents are constant, independent of time. • Direct current is produced by sources such as batteries, thermocouples, solar cells, and others. Direct current may flow in a conductor such as a wire, but can also flow through semiconductors, through a vacuum as in electron or ion beams. Time dependence of current (or voltage) Ohm's Law • deals with the relationship between voltage and current in an ideal conductor. • For many conductors, the electric current which flow through them is directly proportional to the voltage applied to them. U I R • where R is called the resistance • Material that obeys Ohm's Law is called "ohmic" or "linear" because the potential difference across it varies linearly with the current Resistance and conductance l R S where ρ is the resistivity of the material 1 G R G is the conductance of the conductor 1 j E is the conductivity of the material This is also the form of Ohm’s law. Conductivity of electrolytes q0n(b b ) where q0 is charge of each carrier n - concentration of electrolyte molecules (the number of molecules/cubic meter) α - degree of dissociation b – is the electrical mobility of the particle is defined as the ratio of the drift velocity to the magnitude of the electric field tissue cerebrospinal fluid blood muscle tissue brain and nerve tissue fat tissue skin bone without periosteum , m 0.55 1.66 2 14.3 33.3 10 S , m 1.8 0.6 0.5 0.07 0.03 5 10 7 10 7 10 • Galvanization is a method of direct continuous current medical use: low voltage current (up to 80V) and small amperage (up to 50mA)(partial galvanisation: when the current impacts a small area of the body; whole galvanisation: when the current impacts the entire body). • Medicinal electrophoresis is a simultaneous application of direct current (galvanic current) and small amount of drug or combination of drugs. Medicinal electrophoresis • 1) possibility of effect concentration on a surface part of body; 2) long duration of procedure action – drug depot retains for several days; 3) exception of drug effect on alimentary organs; 4) drug introduction into organism in the form of ions, i.e. in active form. Alternating current Alternating current • In alternating current (AC, also ac) the movement of electric charge periodically reverses direction. • In alternating current (AC) circuits the voltage oscillates in a sine wave pattern, varying with time as: U U m sin t where ω is the angular frequency related to the frequency by 2 Properties of Alternating Current • Amplitude. Mathematically, the amplitude of a sine wave is U the value of that sine wave at its peak. This is the maximum value, positive or negative, that it can attain. • Frequency is the number of complete cycles voltage (or current) goes through in a unit time. The frequency of the wave is measured in cycles per second (cycles/sec) and, in normal usage, is expressed in units of Hertz (Hz). In North America (primarily the US and Canada), the AC power system operates at a frequency of 60 Hz. In Europe, including the UK, Ireland, and Scotland, the power system operates at a frequency of 50 Hz. • Period is the time duration of one cycle of the waveform, and is measured in seconds/cycle. AC power at 50 Hz will have a period of 1/50 = 0.02 seconds/cycle. A 60 Hz power system has a period of 1/60 = 0.016667 seconds/cycle. These are often expressed as 20 ms/cycle or 16.6667 ms/cycle, where 1 ms is 1 millisecond = 0.001 second (1/1000 of a second). m Properties of Alternating Current • Wavelength is the distance which the wave moves in one cycle. Electrical signals travel through their wires at nearly the speed of light, which is very nearly 3 × 108 m/s, and is represented mathematically by the letter ‘c‘. c • However, when we speak of an AC power system, it is more useful to refer to the effective voltage or current. This is the rating that would cause the same amount of work to be done (the same effect) as the same value of DC voltage or current would cause. For a sine wave, the effective voltage of the AC power system is (or 0.707 times the peak voltage). The effective voltage is also known as the rms voltage. U ef Um 2 Resistor AC Response Capacitor AC Response Inductor AC Response Series Resonance • The resonance of a series RLC circuit occurs when the inductive and capacitive reactances are equal in magnitude but cancel each other because they are 180 degrees apart in phase.