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- 1. Electric Current, Ohm’s Law, and Electric Circuits ISAT 241 Fall 2002 David J. Lawrence
- 2. Electric Current <ul><li>Consider a bar of material in which positive charges are moving from left to right: </li></ul><ul><li>Electric current is the rate at which charge </li></ul><ul><li>passes through the surface, I avg = Q/ t , </li></ul><ul><li>and the instantaneous current is I = dQ/dt . </li></ul>imaginary surface I
- 3. Electric Current <ul><li>SI unit of charge: Coulomb (C) </li></ul><ul><li>SI unit of current: Ampere (1A= 1C/s) </li></ul><ul><li>A current of 1 ampere is equivalent to 1 Coulomb of charge passing through the surface each second. </li></ul>
- 4. Electric Current <ul><li>By definition , the direction of the current is in the direction that positive charges would tend to move if free to do so, i.e., to the right in this example. </li></ul><ul><li>In ionic solutions (e.g., salt water) positive charges (Na + ions) really do move. In metals the moving charges are negative , so their motion is opposite to the conventional current. </li></ul><ul><li>In either case, the direction of the current is in the direction of the electric field. </li></ul>
- 5. Electric Current <ul><li>Na + ions moving through salt water </li></ul><ul><li>Electrons moving through copper wire </li></ul>E I E I
- 7. Electric Current <ul><li>The electric current in a conductor is given by </li></ul><ul><li>where </li></ul><ul><li>n = number of mobile charged particles </li></ul><ul><li> (“carriers”) per unit volume </li></ul><ul><li>q = charge on each carrier </li></ul><ul><li>v d = “drift speed” (average speed) of </li></ul><ul><li> each carrier </li></ul><ul><li>A = cross-sectional area of conductor </li></ul><ul><li>In a metal, the carriers have charge q e. </li></ul>
- 9. Electric Current <ul><li>The average velocity of electrons moving through a wire is ordinarily very small ~ 10 -4 m/s. </li></ul><ul><li>It takes over one hour for an electron to travel 1 m!!! </li></ul>E I
- 11. Ohm’s Law <ul><li>For metals, when a voltage (potential difference) V ba is applied across the ends of a bar, the current through the bar is frequently proportional to the voltage. </li></ul> <ul><li>The voltage across the bar is denoted: </li></ul><ul><li> V ba = V b V a . </li></ul>area A V b V a E I
- 12. Ohm’s Law <ul><li>This relationship is called Ohm’s Law. </li></ul><ul><li>The quantity R is called the resistance of the conductor. </li></ul><ul><li>R has SI units of volts per ampere. One volt per ampere is defined as the Ohm ( . 1 =1V/A. </li></ul><ul><li>Ohm’s Law is not always valid!! </li></ul>
- 17. Ohm’s Law <ul><li>The resistance can be expressed as </li></ul><ul><li> where </li></ul><ul><ul><li> is the length of the bar (m) </li></ul></ul><ul><ul><li>A is the cross-sectional area of the bar (m 2 ) </li></ul></ul><ul><ul><li> , “Rho”, is a property of the material called the </li></ul></ul><ul><ul><li>resistivity. SI units of ohm-meters ( -m). </li></ul></ul> area A V b V a E I
- 18. Ohm’s Law <ul><li>The inverse of resistivity is called conductivity : </li></ul><ul><li>So we can write </li></ul>
- 19. Resistance and Temperature <ul><li>The resistivity of a conductor varies with temperature (approximately linearly) as </li></ul><ul><li>where </li></ul><ul><ul><ul><li> resistivity at temperature T ( o C) </li></ul></ul></ul><ul><ul><ul><li> o resistivity at some reference temperature T o (usually 20 o C) </li></ul></ul></ul><ul><ul><ul><li> “ temperature coefficient of resistivity”. </li></ul></ul></ul><ul><li>Variation of resistance with T is given by </li></ul>
- 21. Electrical Power <ul><li>The power transferred to any device carrying current I (amperes) and having a voltage (potential difference) V (volts) across it is </li></ul><ul><li>P = VI </li></ul><ul><li>Recall that power is the rate at which energy is transferred or the rate at which work is done. </li></ul><ul><li>Units: W (Watt) = J/s </li></ul>
- 24. Electrical Power <ul><li>Since a resistor obeys Ohm’s Law </li></ul><ul><li>V = IR , we can express the power dissipated in a resistor in several alternative ways: </li></ul>

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