8.5.P20

1. Write Ohm's law in symbols, carefully defining each of the variables.

Symbolically, Ohm's law is best represented as *I * = *V/R*.

Current (*I*) is the rate that charge passes through the object and is measured in amperes (amps). Potential difference (*V*) is the "pressure" the charges are feeling due to a change in energy per charge (volts). Resistance (*R*) is a measure of how much the charge is impeded by the material.

2. Write Ohm's law as a "word equation" expressing a relationship among physical measurements.

In word form, one can state that the current through an object is directly proportional to the potential difference across is and is inversely proportional to the object's resistance.

3. Discuss what you might find in a laboratory about whether all materials obey Ohm's law and show a graph illustrating your results.

"Ohmic" materials would explicitly follow Ohm's law, so a graph of current versus voltage would be linear. A "non-ohmic" material would be non-linear.

In this I-V graph, The blue curve represents and "ohmic" material while the red curve would be non-ohmic. It is interesting to note that at certain potentials, the non-ohmic material can be approximated as linear.

4. Discuss the microscopic mechanism responsible for Ohm's law working in a resistor and identify what characteristics of the material the resistor is made of are relevant for determining the current flow in the resistor.

If we envision the solid as a lattice of atoms that the charges would have to move through, then we can see those atoms that are in the way of the moving electrons would offer resistance to the current and a mechanism for energy loss.

5. If we have a uniform block of material, its mass is dependent on the geometrical properties of the block (its volume) and a property of the material that is independent of the size of the particular bloc (the density). We can then write

(mass) = (density)(volume)

in order to separate those factors.

Consider a cylindrical resistor of cross sectional area, *A*, and length,* L*, carrying an electrical current perpendicular to *A* and parallel to *L*. Write a decomposition of the resistance of the cylinder on the geometrical properties of the resistor (*A* and *L*) and on other properties of the material that are independent of the size and shape of the resistor.

If we consider a cylindrical resistor for the charges to pass through, the resistance would be directly proportional to the resistivity of the material (a property of the material that helps to describe how good a conductor/insulator the material can be), and the length of the cylinder. The resistance would be inversely proportional to the cross-sectional area of the cylinder.

Joe Redish 4/26/10 David Buehrle 11/3/15

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