2 Basic Elements II

2 Basic Elements II - ELEC101 BasicElements34 2010/11Spring...

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ELEC 101 Basic Elements 34 2010/11 Spring 11. Ohm's Law and Resistors When voltage is applied across a piece of material, for example, by a battery, current will flow. For many materials, the amount of current is proportional to the voltage, and the relation is described by Ohm's law : V = I R( I = V / R ) and R is the resistance of the material, with the unit ohm ( ). In a circuit, we use resistors (devices made to have precise resistance) to control current flow. Ohm's law can be written as I = G V with G = 1/R G is the reciprocal of R and is known as the conductance . The unit is mho ( –1 ), or siemen (S).
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ELEC 101 Basic Elements 35 2010/11 Spring 1 ohm = 1 volt / 1 ampere : 1 =1V/1A i(t) - v(t) (or I - V ) characteristics of a resistor slope = di/dv = 1/R i(t) v(t) Time form of Ohm’s law B Resistivity C carbon e i(t) v(t) + metal plate L w t v(t) = i(t) R = resistivity of material (unit : -m) = 1/ is conductivity wt L R Given in exam electron I 2 Example Find I . I = V / R = 4V / 2 = 2A 4V resistor PRS
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ELEC 101 Basic Elements 36 2010/11 Spring Conductivity and resistivity •T w o parallel metal plates with a voltage V applied. A uniform resistive conductor is in between. •N o w Therefore •w h e r e •W e have assumed that and are constant. Sometimes they can vary as a function of z , or even as a function of E h e y are also temperature dependent •M e a s u r e m e n t of very high and very low is difficult E J L V A I ; IR wt R
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ELEC 101 Basic Elements 37 2010/11 Spring Carbon resistors •M o s t common – consists of either bulk carbon composite or thick carbon film
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ELEC 101 Basic Elements 38 2010/11 Spring R = L/A = (1.7  -cm)(1cm)/0.01cm 2 = 170  Cu 1.7  -cm, Al 2.7  -cm Ag 1.6  -cm , Au 2.4  -cm Silver (Ag) wire, is lowest Example Example I V 1cm 1cm 1cm Find the resistance . Given = 1.6  -cm I V 2cm 2cm 1cm Find the resistance. Given = 1.6  -cm Example copper (Cu) wire : = 1.7  -cm, L = 1cm, A = 1mm 2 . Find R. Example 6 1 cm t w A L R . PRS
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ELEC 101 Basic Elements 39 2010/11 Spring 12. Sheet resistance •U s e f u l concept for thin films–there are many such thin films used in circuit elements and in integrated circuit fabrication . These thin films are typically less than 1 m thick. Does not make sense to talk about sheet resistance if thickness is larger s is called the sheet resistivity. Sometimes called the sheet resistance. So sheet resistivity is not an intrinsic value of the material. It depends on the thickness of the film. The dimension of s is Ohm. Its unit is Ohm/square. L/W is called the number of squares Example: A 100nm thick copper film has a sheet resistance of 1.7x10 8 m / 100 nm = 0.17 /sq. So on a silicon chip, a copper line of 2 m width and 1mm long will have a resistance of 0.17 x 1mm / 2 m = 85  Such copper lines are used for routing and interconnecting different parts of the integrated circuit.
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This note was uploaded on 03/27/2011 for the course ELEC 212 taught by Professor Prof.matthewmckay during the Spring '11 term at HKUST.

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2 Basic Elements II - ELEC101 BasicElements34 2010/11Spring...

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