University Physics: Waves and Electricity

University Physics: Waves and Electricity Ch26. Ohm’s Law Lecture 9 Dr.-Ing. Erwin Sitompul http://zitompul.wordpress.com 2014

Homework 7 The rectangular ABCD is defined by its corner points of A(2,0,0), B(0,3,0), C(0,3,2.5), and D(2,0,2.5). Draw a sketch of the rectangular. Given an electric field of E = –2i + 6jN/C, draw the electric field on the sketch from part (a). Determine the number of flux crossing the area of the rectangular ABCD. → ^ ^

Solution of Homework 7 • Projection of ABCD on the xz plane z 3 • Projection of ABCD on the yz plane C 2 D 1 B y 0 1 2 3 1 2 A 3 x

Electric Current • Previously we have discussed electrostatics – the physics of stationary charges. • From this point onward, we will discuss the physics of charges in motion –that is, electric currents. • Electric currents involve many professions, especially engineers. • Electrical engineers are concerned with countless electrical systems such as power systems, lightning systems, and information storage systems.

Electric Current • As we know, there are two kinds of electric charge carriers: the positive charge carrier (hole) and the negative charge carrier (electron). • In a conducting material, a number of electrons are not bounded to the atom and can freely move across the material. This electron is called conduction electron. • A hole is actually the empty state left by a freely moving electron. We define a hole to have a positive charge, in opposite to the electron. • Current is defined as the rate of movement of charge passing a given reference point (or crossing a given reference plane) • Through convention, the direction of hole movement is defined as the direction of current

Checkpoint Consider positive and negative charges moving horizontally through four different pieces of a conductor. (a) Determine the current direction of each piece. (b) Rank the current from highest to lowest. (a) and (c) rightward, (b) and (d) leftward a, b and c tie, d • Can you determine the direction of the fields E? →

Electric Current • Although an electric current is a stream of moving charges, not all moving charges constitute an electric current. • An electric current through a given surface exist only when there is a net flow of charge through that surface. • If an electric field exists, the charge carriers (conducting electrons and holes) will move under the influence of the field. • Flow of carriers will stop when the electric field is zero or the potential difference is zero.

Electric Current • The SI unit for current is the coulomb per second (C/s) or the ampere (A). • Current is a scalar quantity. We do not need direction to define it. • Yet, we know that current will flow in the same direction as the electric field, or from higher potential to lower potential. • We often represent the current direction with an arrow near a conductor (wire, cable, etc).

Checkpoint The figure below shows a portion of a circuit. What are the magnitude and direction of the current I in the lower right-hand wire? 5 A 6 A 8 A The magnitude of the current is 8 A, flowing from left to right

Resistance and Resistivity • One of the characteristics of a conductor is the electrical resistance. • We determine the resistance between any two points of a conductor by applying a potential difference V between those points and measuring the current i that results. • The SI unit for resistance is the volt per ampere. This combination, however, occurs so often that it is given a special name ohm (symbol Ω).

Resistance and Resistivity • A conductor whose function in an electric circuit is to provide a specified resistance is called a resistor. • In a circuit diagram, the resistor is represented by the symbols: • We can rewrite the last equation to become: • For a given V, • The greater the resistance, the smaller the current • The smaller the resistance, the greater the current

Resistance and Resistivity • The resistivity is characteristic for each material. It depends on the properties of the material and on temperature. • The next table lists the resistivities of some materials at 20 °C.

Resistance and Resistivity • The resistivity is denoted with ρ. The SI unit of resistivity is ohm-meter (Ωm). • We can also speak of the conductivity σ of a material. This is simply the reciprocal of its resistivity, so: • The SI unit of conductivity is (Ωm)–1. Sometimes the unit mhos per meter is used.

Calculating Resistance from Resistivity • Distinction: • Resistance is a property of an object. • Resistivity is a property of a material • Let A be the cross-sectional area of the wire of length L, and let a potential difference V exist between its ends. • The resistance of the wire is given by:

Checkpoint The figure here shows three cylindrical copper conductors along with their face areas and lengths. Rank them according to the current through them, greatest first, when the same potential difference V is placed across their lengths. (a) and (c) tie, then (b) • For the same potential difference V, • The resistance >>, the current << • The resistance <<, the current >>

Variation with Temperature • The values of resistivity varies with temperature. • The next figure shows the variation of this property for copper over temperature. • The relation between temperature and resistivity for copper –and for metal in general– is fairly linear. • For such linear relations, the following empirical approximation is good enough for most engineering purposes: • T0 = 20°C = 293 K (room temperature) • α is the temperature coefficient, (°C)–1, (see table)

Color-Coding of Resistor Identification 1 0 4 ±10% ±5% 1 2 6 3 3 9 0 ±1%

Homework 8 A rectangular block of iron has dimensions 1.2 cm  15 cm  1.2 cm. The temperature of the surrounding air is 20 °C. A potential difference is to be applied to the block between parallel sides. What is the resistance of the block if the two parallel sides are the square ends (with dimensions 1.2 cm  1.2 cm)? The temperature of the iron block increases up to 35 °C due to the flowing current. What is the resistance of the block now?

Homework 8A 1. A rectangular block of copper has dimensions 1.2 cm  15 cm  1.2 cm. The temperature of the surrounding air is 25 °C. A current of 2.2 mA flows through the block between parallel sides. What is the resistance of the block if the two parallel sides are the two rectangular sides (with dimensions 1.2 cm  15 cm)? The temperature of the copper block increases up to 27°C due to the flowing current. What is the potential difference between the parallel sides? A composite wire of unknown material has a resistance of 8.0 Ω. It is then molded and reformed so that its new length is four times its original length. Find the resistance of the wire now, if it may be assumed that the density and resistivity of the composite are unchanged.

University Physics: Waves and Electricity