Current

In terms of the current density

For a uniform current density parallel to the area element

Ohm’s Law

Practical versionwhere the resistance is

Chapter 27: Current and Resistance

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Ohmic material Nonohmic material

Example Problem Lightning strikes the ground with a current of 100 kA. A person and a cow are each a radial distance D=60.0 m from the lightning strike. The current spreads through the ground uniformly over a hemisphere centered on the strike point. The person’s feet are separated by radial distance rper=0.50 m; the cow’s front and rear hooves are separated by the radial distance rcow=1.50 m. The resistivity of the ground is gr=100 m. The resistance both across the person, between left and right feet, and across the cow, between front and read hooves, is R=4.00 k. What are the currents through the person and through the cow?

Microscopic Description of Current and Ohm’s Law

Consider a conductor with cross sectional area A and a segment length xIf there is no potential difference across it, the electric field in the wire is zero and therefore the current is zeroHowever, there are electrons moving within the conductorThese conduction electrons move

in random directions, but at high speeds ~106 m/s

x

No net displacement of the electrons no current no electric field However, if a V is applied then there is an electric field in the conductor and a currentConsidering the current at a microscopic level, there is a volume element of Ax with n total number of charge carriers per unit volume each with positive charge qThe total charge in the volume element is

They move with a constant speed, the drift speed vd

xqnAQ

In a vacuum with a uniform electric field, electrons move in a straight line in the opposite direction of the field lines However, in a conductor, the electrons travel for short distances (~40 nm), in random directions until they encounter and atom, where the electron is scattered in a random direction Nevertheless, the electrons move slowly in the direction opposite the electric field at the drift speed (~10-4 m/s)The drift speed of electrical conduction can be understood through the Drude model which applies classical mechanics

Example Problem 27.25

If the magnitude of the drift velocity of free electrons in a copper wire is 7.84x10-4 m/s, what is the electric field in the conductor?

Variation of Resistivity and Resistance with Temperature

The values of most physical properties of materials vary with temperature For a conductor, it is found, over a limited temperature range, that this variation is linear in temperature

)](1[)( 00 TTT 0 is the resistivity at room

temperature T0=20 C and is the temperature coefficient of resistivity. It is given in Table 27.1 and has units of 1/C

Example Problem 27.29

A certain light bulb has a tungsten filament with a resistance of 19.0 when cold and 140 when hot. Assume that the resistivity of tungsten varies linearly with temperature even over the large temperature involved here, and find the temperature of the hot filament. Assume the initial temperature is 20.0 C.

Power in Electrical Circuits

A circuit is a closed loop (usually consisting of high conductivity wire) with a battery and one or more circuit elementsWe assume now that the resistance in the wire is small and can be neglected

a

b

Mechanical Analogy

Example Problem 27.36

A toaster is rated at 600 W when connected to a 120-V source. What current does the toaster carry, and what is its resistance?