From: https://ece.uwaterloo.ca/~dwharder/Analogy/Resistors/ Current = I = dQ/dt, unit is C/Sec which is called Ampere, A w/o proof: I=nqAvd Example: A copper wire (2mm dia) carries 10A current. If 3 =8.9x10 kg/m3, amu = 63.5 gr/mole and there is one electron/atom, calculate: •Number of electrons/m3 •Drift velocity PHYS42-9-24-2015 Page 1 •Drift velocity This is the AVERAGE speed of electrons in the wire. Why is it so low? example: An electron is orbiting in a Circle of radius R. What is the current associated with this motion? Electron is moving with speed of V. PHYS42-9-24-2015 Page 2 Symbol for resistance is Symbol for Battery is Symbol for Capacitor is This means VARIABLE PHYS42-9-24-2015 Page 3 Conductivity Unit of Conductivity? Example: A 8mm diameter plastic wire (L=1m) is coated with gold to a thickness of 1 micron. If for gold is 2.44x10-8 ohms-m, what is the resistance of wire end to end? A wire is drawn to 3 times of it's original Length. what is the ratio of new resistance to the old one? PHYS42-9-24-2015 Page 4 R=R0(1+α(T)) or =0(1+α(T)) NOTE: R0 and 0 are not resistance and resistivity at 0 degrees. They are the constant at the temperature given when α is specified wrong way: PHYS42-9-24-2015 Page 5 Right Way: Current Density Use of Resistance for "strain. Gauge" This section will not be in your test. PHYS42-9-24-2015 Page 6 This section will not be in your test. After Some math! Modeling R PHYS42-9-24-2015 Page 7 Modeling R Challenging problem: A resistor is to be made by combining two rods, one made from graphite and the other from Iron, to have total resistance of 1000 ohm and to be independent of the temperature. Both rods should have radius of 1 mm. Ignore length change due to temperature. -3 -1 -3 -1 αC= -7.5x10 C and αFe = +5x10 C -5 -8 C=3.5x10 ohms-m and Fe =10x10 ohms-m In a gold plating experiment, a 6x10 cm2 sheet is to be plated with gold to a thickness of 10 micron. The plate to plate resistance of the apparatus is measured to be 2 ohms. How long does experiment take? Use density of gold as 19300 Kg/m3. PHYS42-9-24-2015 Page 8 In Capacitors (and later for inductors), we talk about stored energy. In resistors, we talk about power, P=IV=RI2=V2/R Wire connecting a generator to a small town is carrying 2000A current with voltage of 800KV. The length of the wire is 600Km. The resistance of the wire is rated as 0.4 ohms/Km. Calculate the efficiency of the power delivery system. PHYS42-9-24-2015 Page 9 PHYS42-9-24-2015 Page 10 Resistors in Series PHYS42-9-24-2015 Page 11 Resistors in Series Resistors in Parallel Example PHYS42-9-24-2015 Page 12 Example PHYS42-9-24-2015 Page 13 Another Example Two, very thin spherical shells (R1=3 cm and R2=8 cm)are used for constructing a resistor. The space between two shells is filled with a material with resistivity of 40 ohms-m. Calculate the resistance between inner and outer conductor. Lets choose a spherical shell (radius r), PHYS42-9-24-2015 Page 14 .