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Direct Current (DC) Circuits 1 PHYS 0212 DC Circuits 1 1 Direct Current (DC) Circuits 1 This experiment has four parts: 1. Construct an Ammeter to measure electrical current. Using a Galvanometer { 2. Construct an Ohmmeter to measure electrical resistance. 3. Construct a Voltmeter to measure voltage. 4. Measure the internal resistance of a galvanometer. Electrical charge is a fundamental property of matter, like mass, and may be either positive or negative. The unit of electrical charge is the Coulomb (C). 1.0 C 1.602 1019 electrons Electrical Current (I) – The amount of charge flowing past a given point per unit time. Coulomb Ampere (amp or A) second PHYS 0212 DC Circuits 1 2 Voltage (V) – The energy per unit of charge. Joule Volt (V) Coulomb The Voltage and the Current are related by Ohm’s Law: V IR Volt R = Resistance, units are: Ohm () Amp A circuit is a closed path for electrical current. + - 1. Electrons gain potential energy in the battery. 2. They leave the positive end of the battery and travel to the filament of the light bulb. 3. They lose potential energy in the filament by converting it to light and heat. 4. The electrons return to the negative end of the battery and gain more potential energy. PHYS 0212 DC Circuits 1 3 A circuit is often drawn using a schematic – Lines represent wires and symbols represent circuit elements. If the voltage of the batter is V = 1.5 V and the resistance is R = 100 , what is the current in the circuit? V IR I V I R R 1.5 V I 0.015 A 100 + I - I 15 mA V PHYS 0212 DC Circuits 1 4 Resistors in a circuit may be connected two different ways: series and parallel. Series –The current through each device is the same but the voltage change across each device may be different. R1 R2 V IR1 IR2 I R1 R2 Rs is a single resistor that can effectively replace R1 and R2. IRs I R1 R2 I IRs I R1 R2 - + V Note that adding resistors in series increases the effective resistance. Rs R1 R2 In general, if there are N resistors in series, then the effective resistance for all of them will be: Rs R1 R2 R3 PHYS 0212 DC Circuits 1 RN 5 Parallel –The voltage across each device is the same but the current through each device may be different. R2 V IRp I2 Rp is a single resistor that can effectively replace R1 and R2. R1 V V V R p R1 R2 I I1 I 2 I1 I I + V I Rp V Note that adding resistors in parallel decreases the effective resistance. 1 1 1 Rp R1 R2 In general, if there are N resistors in parallel, then the effective resistance for all of them will be: 1 1 1 1 Rp R1 R2 R3 PHYS 0212 DC Circuits 1 1 RN 6 Example: What is the effective resistance of this circuit? Start with the parallel combination: 1 1 1 1 1 1 Rp R2 R3 200 300 120 R2=200 R1=100 Rs=220 Rp=120 R3=300 Rp 120 Now calculate the series combination: Rs R1 Rp Rs 100 120 + Rs 220 V PHYS 0212 DC Circuits 1 7 What is the effective resistance between points x and y? 300 2000 600 x y 500 200 a) 80 b) 3600 c) 764 d) 500 PHYS 0212 DC Circuits 1 8 Galvanometer A device that measures electrical current in a circuit. A galvanometer must be placed in series in a circuit so that the current passes through the meter. For this reason the internal resistance of the galvanometer Rm should be as small as possible, ideally zero ohms. G Rm R The arrow means the resistor R is variable. + G Rm This is the basic circuit you will use for the first three parts of the lab. Ohm’s law for this circuit is: V I R Rm - V PHYS 0212 DC Circuits 1 9 The power through the resistance substitution box must not exceed 2 Watts. P IV (2 W) I 5 V I 0.40 A 400 mA PHYS 0212 DC Circuits 1 V IR V 5V R I 0.4 A R 13 10 A word of advice. Adjust the resistance on the decade box to get an even value of the current. 2660 2497 It is difficult to estimate the value of the current between the tick marks. However, if you adjust the resistance so the needle falls right on a tick mark each time then your results will be much more accurate. PHYS 0212 DC Circuits 1 11 Construction of an Ammeter An ammeter measures electrical current I. V I R Rm R Solve Ohm’s law for R. G R V Rm I Rm + - Make the substitution: x 1 I R Vx Rm V PHYS 0212 DC Circuits 1 12 R Vx Rm Make a plot of R versus x. slope V intercept Rm The voltage of the power supply. The internal resistance of the galvanometer. PHYS 0212 DC Circuits 1 13 Construction of an Ohmmeter An ohmmeter measures electrical resistance R. Same equation as before: R Vx Rm The values of V and Rm come form part one. R G Rm + V - In this part of the lab you will put known values of resistance into the circuit and use this equation to calculate R. You will use this circuit to measure individual resistors as well as series and parallel combinations of resistors. PHYS 0212 DC Circuits 1 14 Construction of an Voltmeter An voltmeter measures voltage V. The voltage may be determined with this equation: V I R Rm R G Rm + - V Say I 2 mA and R m 10 The value of Rm comes form part one and the resistance R is preset. In this part of the lab you will put known sources of voltage into the circuit and use this equation to calculate V. The preset value of R may be determined using Ohm’s law: If Vmax 30 V and I max 5 mA then V 2 10-3 A 5990 10 V 12.0 V then R Vmax 30 V Rm 10 5990 -3 I max 5 10 A PHYS 0212 DC Circuits 1 15 The Internal Resistance of the Galvanometer You will determine the internal resistance of the galvanometer Rm from the intercept of R versus x (1/I), but how accurate is it? This procedure will determine Rm more directly. Step 1 – Adjust the external resistor R1 until the current through the galvanometer is 4 mA. R1 V IA R1 Rm G Rm + V R2 - Step 2 – Add a second external resistor R2 in parallel with the galvanometer and adjust it until the current through the galvanometer is 2 mA. V IB Rm R2 R1 R R 2 m PHYS 0212 DC Circuits 1 Rm R2 1 1 1 Rm R2 Rm R2 16 Assume that R2 Rm 10, R1 1000 and that V 5 V. IA V 5V 5V 4.00 mA R1 Rm 1240 10 1250 IB I A V V 5V 5V IB 4.02 mA 1 Rm Rm R1 2 Rm 1240 5 1245 R1 R R m m This tells us that when we add R2 to the circuit the total current stays approximately the same (only 0.4% difference). So basically, we can turn this around and say that when we adjust R2 such that the current through the galvanometer is cut in half then: R2 Rm PHYS 0212 DC Circuits 1 17 PHYS 0212 DC Circuits 1 18