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Ohm’s Law

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Objective of Lecture Describe how material and geometric properties determine the resistivity and resistance of an object. Chapter 2.1 Explain the relationship between resistance, current, and voltage (Ohms Law). Chapter 2.1 Discuss what a short circuit and open circuit mean using Ohms Law. Chapter 2.1 Explain the relationship between resistance and conductance. Chapter 2.1 Derive the various equations used to calculate the power dissipated by a resistor. Chapter 2.1

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Resistivity, Resistivity is a material property Dependent on the number of free or mobile charges (usually electrons) in the material. In a metal, this is the number of electrons from the outer shell that are ionized and become part of the ‘sea of electrons’ Dependent on the mobility of the charges Mobility is related to the velocity of the charges. It is a function of the material, the frequency and magnitude of the voltage applied to make the charges move, and temperature.

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Resistivity of Common Materials at Room Temperature (300K) Material Resistivity ( -cm) Usage Silver1.64x10 -8 Conductor Copper1.72x10 -8 Conductor Aluminum2.8x10 -8 Conductor Gold2.45x10 -8 Conductor Carbon (Graphite)4x10 -5 Conductor Germanium0.47Semiconductor Silicon640Semiconductor Paper10 Insulator Mica5x10 11 Insulator Glass10 12 Insulator Teflon3x10 12 Insulator

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Resistance, R Resistance takes into account the physical dimensions of the material where: L is the length along which the carriers are moving A is the cross sectional area that the free charges move through.

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Ohm’s Law Voltage drop across a resistor is proportional to the current flowing through the resistor Units: V = A where A = C/s

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Short Circuit If the resistor is a perfect conductor (or a short circuit) R = 0 , then v = iR = 0 V no matter how much current is flowing through the resistor

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Open Circuit If the resistor is a perfect insulator, R = ∞ then no matter how much voltage is applied to (or dropped across) the resistor. A

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Conductance, G Conductance is the reciprocal of resistance G = R -1 = i/v Unit for conductance is S (siemens) or (mhos) G = A /L where is conductivity, which is the inverse of resistivity,

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Power Dissipated by a Resistor p = iv = i(iR) = i 2 R p = iv = (v/R)v = v 2 /R p = iv = i(i/G) = i 2 /G p = iv = (vG)v = v 2 G

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Power (con’t) Since R and G are always real positive numbers Power dissipated by a resistor is always positive The power consumed by the resistor is not linear with respect to either the current flowing through the resistor or the voltage dropped across the resistor This power is released as heat. Thus, resistors get hot as they absorb power (or dissipate power) from the circuit.

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Short and Open Circuits There is no power dissipated in a short circuit. There is no power dissipated in an open circuit.

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Summary Resistivity is a fundamental material property while the material properties and the geometry of the component determine its resistance. Ohms Law: The force required to have a specific current flow through a resistor is given by v = i R. This is an important relationship (learn it). There is zero power associated with short circuit and open circuit since a short circuit has no voltage drop and an open circuit has no current flowing across it. Conductance (conductivity) is the inverse of resistance (resistivity).

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Summary (con’t) The power dissipated by a resistor can be written as: The power dissipated by a resistor is not linear with either the voltage across the resistor or the current flowing through the resistor.

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