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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 Two parallel metal plates with a voltage V applied. A uniform resistive conductor is in between. Now Therefore where We have assumed that and are constant. Sometimes they can vary as a function of z , or even as a function of E They are also temperature dependent Measurement of very high and very low is difficult E J L V E A I J ; IR I A L V wt L A L A L R
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ELEC 101 Basic Elements 37 2010/11 Spring Carbon resistors Most 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 1 cm 6 1 t t w w A L R . . 6 1 cm 1 cm 6 1 t t w w A L R . . PRS
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