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PHYS - 321 ELEMENTARY ELECTRONiCS • RESISTORS • KIRKOFFS LAW and LOOP-MESH METHOD • VOLTAGE DIVIDER • INTERNAL RESISTANCE and OUTPUT IMPEDANCE • HOW TO MEASURE OUTPUT IMPEDANCE OF A DEVICE RESISTORS •Materials have different resistivities ρ • R = ρ (L/A) = resistance L ρ A σ=1/ρ Kirchoffs Laws(1) (1) Let I run CW in loops. (2) Add the emfs. (3) Subtract the voltage drops. V V i1 i R1 R i2 R2 +V-iR = 0 +V-i1 R1 +i2 R1 = 0 0 -i2 R2 -i2 R1 +i1 R1 = 0 V = i1 R1 -i2 R2 0 = -i1 R1 +i2 (R1+R2) Voltage Divider V R1 Vout i R2 V-I R1 -I R2 = 0 V=I(R1+R2) I= V/(R1+R2) Vout = I R2 = {R2/(R1+R2)} V Voltage drop on ith resistor is proportional to ratio of Ri to Rtot! Vi = {Ri/Rtot} V ΔV1 ={R1/(R1+R2)} V ΔV2 ={R2/(R1+R2)} V Output Impedance • • • Every Source of Emf has some small internal resistance. A signal generator has an internal resistance called output Impedance z. ( z~50 Ohm ). A voltage divider circuit can be used to measure r and z. Adjust R until ΔVR=1/2V ! Then R = z ! battery Sine Generator r V i R - z + R Input Impedance • All input devices has some small internal resistance to the current flowing into it. • A voltmeter has a high input impedance to limit the current flowing in to the measuring device. • An ammeter wants to divert all the current into it and therefore has a very low input impedance. V A 1MΩ + f u s e 1Ω - + - Thevenin's Theorem(1) Thevenin's Theorem(2)