Electrical Current Inexact definition: The rate of flow of charge How would you make this definition more precise ? + - - + - + - + - + - - + Although the charge flowing is electron charge (i.e. negative charge), the direction of electric current is defined as the direction of flow of positive charge 1 Electrical Current Inexact definition: The rate of flow of charge How would you make this definition more precise ? Lets consider the following thought experiment. You want to count the number of fish flowing down a river. You would: pick a location on the river, then define a cross-sectional area (perpendicular to the flow of the water) and then you would count the net flow by counting: The number of fish swimming down river The number of fish swimming up river. Definition: The rate of net flow of electric charge through a cross- sectional area that is perpendicular to the direction of flow. 2 Electrical Current Definition: The rate of net flow of electric charge through a cross- sectional area A that is perpendicular to the direction of flow. In the drawing below to get the net flow of charge to the right: add up all the positive charge flowing to the right continue adding negative charge flowing to the left + - - + - + - + - + - - + 3 A Model for Electric Current Lets denote the net charge flowing through this area A in a time interval t as: Q The electric current is then: Q I= t The instantaneous current is obtained by considering smaller and small time intervals, i.e. Q dQ I=lim 0 = t t dt The units for current is called an Ampere. Ampere is a derived unit. 1 1 C A= 1 s 4 Electrical Current Definition: The rate of net flow of electric charge through a cross- sectional area A that is perpendicular to the direction of flow. In the drawing below to get the net flow of charge to the right: add up all the positive charge flowing to the right continue adding negative charge flowing to the left + - - + - + - + - + - - + In electrolytes (like battery fluid), there can be both positive and negative charge carriers. 5 Relating Macroscopic (electrical current) to Microscopic (density of charge carriers) Consider a section of the cylindrical wire below of length x In time t a charge carrier moves a distance x=vd t Here v d is called the drift velocity of the charge carrier. x + - - + - + - + - + - - + vd Consider a section of the cylindrical wire below of length 6 Relating Macroscopic (electrical current) to Microscopic (density of charge carriers) Lets say we know the microscopic density of charge carriers n (this would be the number of charge carriers per unit volume) and the charge on each charge carrier. Q We want to derive an expression for the macroscopic current I= t x + - - + - + - + - + - - + vd 7 Relating Macroscopic (electrical current) to Microscopic (density of charge carriers) The total charge in the section of interest: Q=number of charge carriers xcharge per carrier =n A xq Q Q=n A vd t q or I= =n A v q t d x + - - + - + - + - + - - + vd The current is proportional to the cross-sectional area of the wire. All the other quantities in the equation are microscopic quantities. 8 Relating Macroscopic (electrical current) to Microscopic (density of charge carriers) The current is proportional to the cross-sectional area of the wire. All the other quantities in the equation are microscopic quantities. So we can define a current density I J= =n v q A d which consists of only microscopic quantities x + - - + - + - + - + - - + vd 9 Example 21.1 Drift speed in a copper wire 12-gauge copper wire in a typical residential building has a cross-sectional area of 3.3 x 10 -6 m 2. If it carries a current of 10 A, what is the drift speed of the electrons ? Assume that each copper atom contributes one free electron to the current. Take the density of copper as 8.95 g/cm 3. Also known: Atomic mass of copper is 63.5 g/mole One copper atom has 29 protons and 34 neutrons So one copper atom has how many electrons ?? Do in class 10 Electrical Resistance Definition: The electrical resistance of a conductor is the ratio of the potential difference across it to the current that flows as a result of that potential difference. V R= I Slope is 1/R It turns out that for a conductor that the relationship between current and the potential difference is linear. For a semiconductor this relationship is not linear. The resistance is larger for smaller currents than for large ones. 11 Electrical Resistance Definition: The electrical resistance of a conductor is the ratio of the potential difference across it to the current that flows as a result of that potential difference. V R= I Slope is 1/R It turns out that for a conductor that the relationship between current and the potential difference is linear. For a semiconductor this relationship is not linear. The resistance is larger for smaller currents than for large ones. For an insulator, this resistance is very large. For a superconductor, the resistance is very small. 12.