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Electric Current, Ohm’s Law, and Electric Circuits

Electric Current, Ohm’s Law, and Electric Circuits. ISAT 241 Fall 2002 David J. Lawrence. I. imaginary surface. Electric Current. Consider a bar of material in which positive charges are moving from left to right:. Electric current is the rate at which charge

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Electric Current, Ohm’s Law, and Electric Circuits

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

  2. I imaginary surface Electric Current • Consider a bar of material in which positive charges are moving from left to right: • Electric current is the rate at which charge passes through the surface, Iavg = DQ/Dt, and the instantaneous current is I = dQ/dt.

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

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

  5. E I E I Electric Current • Na+ ions moving through salt water • Electrons moving through copper wire

  6. Electric Current • 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 vd = “drift speed” (average speed) of each carrier A = cross-sectional area of conductor • In a metal, the carriers have charge q = -e.

  7. I E Electric Current • The average velocity of electrons moving through a wire is ordinarily very small ~ 10-4 m/s. • It takes over one hour for an electron to travel 1 m!!!

  8. I A area E Va Vb Ohm’s Law • For metals, when a voltage (potential difference) Vba is applied across the ends of a bar, the current through the bar is frequently proportional to the voltage. l • The voltage across the bar is denoted: • Vba = Vb-Va .

  9. Ohm’s Law • This relationship is called Ohm’s Law. • 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 (W). 1W=1V/A. • Ohm’s Law is not always valid!!

  10. I A area E Va Vb Ohm’s Law • The resistance can be expressed as where l is the length of the bar (m) A is the cross-sectional area of the bar (m2) r, “Rho”, is a property of the material called the resistivity. SI units of ohm-meters (W-m). l

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

  12. Resistance and Temperature • The resistivity of a conductor varies with temperature (approximately linearly) as where r = resistivity at temperature T (oC) ro = resistivity at some reference temperature To (usually 20oC) a = “temperature coefficient of resistivity”. • Variation of resistance with T is given by

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

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

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