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Resistance and Resistivity Resistance and Resistivity Resistivity, what is it? Resistivity is the opposite of conductivity, it’s a measure of how effectively a material slows down the flow of electricity. Insulators have a high resistivity rating. Materials such as metals and other conductors have a low resistivity rating. Resistance and Resistivity A conductor’s Resistance is defined as the ratio of the Applied Voltage to the Current produced. R = V/I Scalar Units: Ohm [Ω] = [V/A] Resistance and Resistivity Resistance can be calculated for any object. Good conductor – low resistance Poor conductor –high resistance All circuit elements have some resistance. The resistance of connecting wire leads is considered negligible. Resistance and Resistivity Resistance The geometry of the resistor matters L R=ρ A Length Area Resistivity: (units m) Increase the Length, flow of electrons impeded Increase the cross-sectional Area, flow enhanced Resistance and Resistivity For a wire of length l and cross-sectional area A the resistance R: Is proportional to l And inversely proportional to A The constant ρ (rho) Is known as the resistivity. l R A Resistance and Resistivity Increasing the cross-sectional area increases the number of available electrons. Resistance and Resistivity Resistance and Resistivity Resistivity l R A Therefore, the units of resistance are: m R m 2 (Ohms) m Resistivity has units of Ohm· meters ( · m) Resistance and Resistivity Resistance and Resistivity Resistance and Resistivity Resistivity and temperature. The resistance and resistivity changes with temperature, therefore resistivity at quoted at a specific temperature The resistance is proportional to the length l and inversely proportional to the cross-sectional area A, the material the conductor is made from, and the temperature. Resistance and Resistivity Superconductivity Below a certain critical temperature, Resistance becomes ZERO, allowing current to exist without energy wasted. Superconductivity, although predicted and discovered a century ago has only become useful recently due to the development of rare-earth conductive ceramics. Superconductive wires are used in the electromagnets of MRI machines. Resistance and Resistivity Two wires, A and B, are made of the same metal and have equal length, but the resistance of wire A is four times the resistance of wire B. How do their diameters compare? a. b. c. d. e. dA dA dA dA dA = = = = = 4 dB 2 dB dB ½ dB ¼ dB l R A Resistance and Resistivity A wire of resistance R is stretched uniformly (keeping its volume constant) until it is twice its original length. What happens to the resistance? a. it increases by a factor 4 b. it increases by a factor 2 c. it stays the same d. it decreases by a factor 2 e. it decreases by a factor 4 Resistance and Resistivity Find the resistance of a piece of copper with a diameter of 1 mm and a length of 1 cm -8 -2 l (3 x 10 )(1 x 10 ) 12 -4 R = = x 10 -3 2 A ( (.5 x 10 ) Resistance and Resistivity Bolbo the gold broker from Baghdad has just received a gold bullion bar for his birthday from his brother Bob. The face of the bar is 5 cm on both sides, and the length is 20 cm. The resistance between faces A and B is measured to be 0.8 micro-ohms. Bolbo the broker assumes that the bullion is gold if the measured resistance is within +/- 10% of the theoretical value. Is the material gold or is it bogus? R L / A (2.4 x108 m)(.2m) / .052 m 2 ) 1.92 x106 =1.92 u don’t try to cash it in! B Resistance and Resistivity A wire 10 m long consists of 5 m of copper followed by 5 m of aluminum of equal diameter of 1 mm. A voltage difference of 80 V is placed across the composite wire. a. What is the total resistance of the wire? b. What is the current flow through the wire? Resistance and Resistivity Summary