Electric Current, Ohm’s Law, and Electric Circuits ISAT 241 Fall 2002 David J. Lawrence

Electric Current u Consider a bar of material in which positive charges are moving from left to right: imaginary surface I u Electric current is the rate at which charge passes through the surface, I avg =  Q/  t, and the instantaneous current is I = dQ/dt.

Electric Current u SI unit of charge: Coulomb (C) u SI unit of current: Ampere (1A= 1C/s) u A current of 1 ampere is equivalent to 1 Coulomb of charge passing through the surface each second.

Electric Current u 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. u 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. u In either case, the direction of the current is in the direction of the electric field.

Electric Current u Na + ions moving through salt water u Electrons moving through copper wire EI E I

Electric Current u The electric current in a conductor is given by where n = number of mobile charged particles (“carriers”) per unit volume q = charge on each carrier v d = “drift speed” (average speed) of each carrier A = cross-sectional area of conductor  In a metal, the carriers have charge q  e.

Electric Current u The average velocity of electrons moving through a wire is ordinarily very small ~ m/s. u It takes over one hour for an electron to travel 1 m!!! E I

Ohm’s Law u 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. area A VbVb VaVa E I  The voltage across the bar is denoted: V ba = V b  V a.

Ohm’s Law u This relationship is called Ohm’s Law. u The quantity R is called the resistance of the conductor.  R has SI units of volts per ampere. One volt per ampere is defined as the Ohm ( . 1  =1V/A. u Ohm’s Law is not always valid!!

Ohm’s Law u The resistance can be expressed as where is the length of the bar (m) A is the cross-sectional area of the bar (m 2 ) , “Rho”, is a property of the material called the resistivity. SI units of ohm-meters (  -m). area A VbVb VaVa E I

Ohm’s Law u The inverse of resistivity is called conductivity: u So we can write

Resistance and Temperature u The resistivity of a conductor varies with temperature (approximately linearly) as where  resistivity at temperature T ( o C)  o  resistivity at some reference temperature T o (usually 20 o C)  “temperature coefficient of resistivity”. u Variation of resistance with T is given by

Electrical Power u The power transferred to any device carrying current I (amperes) and having a voltage (potential difference) V (volts) across it is P = VI u Recall that power is the rate at which energy is transferred or the rate at which work is done. u Units: W (Watt) = J/s

Electrical Power u Since a resistor obeys Ohm’s Law V = IR, we can express the power dissipated in a resistor in several alternative ways: