Direct Current (DC) Circuits NOTE: There are short answer analysis questions in the Participation section the informal lab report. emember to include these answers in your lab notebook as they will be part of your participation grade. PHYS 0219 DC Circuits 1
Direct Current (DC) Circuits This experiment has five parts: Using a Galvanometer { 1. Construct an Ammeter to measure electrical current. 2. Construct an Ohmmeter to measure electrical resistance. 3. Construct a oltmeter to measure voltage. 4. Measure the internal resistance of a galvanometer. 5. C Circuits. 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). 19 1.0 C 1.602 10 electrons Electrical Current () The amount of charge flowing past a given point per unit time. Ampere (amp or A) Coulomb second PHYS 0219 DC Circuits 2
oltage () The energy per unit of charge. olt () Joule Coulomb The oltage and the Current are related by Ohm s Law: = esistance, units are: olt 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 0219 DC Circuits 3
A circuit is often drawn using a schematic Lines represent wires and symbols represent circuit elements. f the voltage of the batter is = 1.5 and the resistance is = 100, what is the current in the circuit? 1.5 0.015 A 100 + - 15 ma PHYS 0219 DC Circuits 4
esistors 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. 1 2 + - 1 2 1 2 s is a single resistor that can effectively replace 1 and 2. s s 1 2 1 2 s 1 2 Note that adding resistors in series increases the effective resistance. n general, if there are N resistors in series, then the effective resistance for all of them will be: s 1 2 3 N PHYS 0219 DC Circuits 5
Parallel The voltage across each device is the same but the current through each device may be different. 2 p p 2 1 1 + - Note that adding resistors in parallel decreases the effective resistance. p is a single resistor that can effectively replace 1 and 2. 1 2 1 1 1 p 1 2 1 2 n general, if there are N resistors in parallel, then the effective resistance for all of them will be: 1 1 1 1 1 p PHYS 0219 DC Circuits 6 p 1 2 3 N
Example: What is the effective resistance of this circuit? Start with the parallel combination: 1 =100 s =220 1 1 1 1 1 1 200 300 120 p 2 =200 p =120 2 3 p 120 Now calculate the series combination: + - 3 =300 s 1 100 120 s s 220 p PHYS 0219 DC Circuits 7
What is the effective resistance between points x and y? 2000 300 x 500 600 y 200 a) 80 b) 3600 c) 764 d) 500 PHYS 0219 DC Circuits 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 m should be as small as possible, ideally zero ohms. m G The arrow means the resistor is variable. + - m G This is the basic circuit you will use for the first three parts of the lab. Ohm s law for this circuit is: m PHYS 0219 DC Circuits 9
The power through the resistance substitution box must not exceed 2 Watts. P 5 (2 W) 5 0.4 A 0.40 A 400 ma 13 PHYS 0219 DC Circuits 10
A word of advice. Adjust the resistance on the decade box to get an even value of the current. 2660 2497 t 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 0219 DC Circuits 11
Construction of an Ammeter An ammeter measures electrical current. m m G Solve Ohm s law for. m + - Make the substitution: x 1 x m PHYS 0219 DC Circuits 12
x m Make a plot of versus x. slope The voltage of the power supply. intercept m The internal resistance of the galvanometer. PHYS 0219 DC Circuits 13
Construction of an Ohmmeter An ohmmeter measures electrical resistance. Same equation as before: x m + - m G The values of and m come form part one. n this part of the lab you will put known values of resistance into the circuit and use this equation to calculate. You will use this circuit to measure individual resistors as well as series and parallel combinations of resistors. PHYS 0219 DC Circuits 14
A voltmeter measures voltage. + - Say 2 ma and 10 m Construction of an oltmeter m G -3 10 then 2 10 A 5990 12.0 The voltage may be determined with this equation: m The value of m comes form part one and the resistance is preset. n this part of the lab you will put known sources of voltage into the circuit and use this equation to calculate. The preset value of may be determined using Ohm s law: f max and max 30 5 ma max then m 10-3 max 510 A PHYS 0219 DC Circuits 15 30 5990
1 + - The nternal esistance of the Galvanometer You will determine the internal resistance of the galvanometer m from the intercept of versus x (1/), but how accurate is it? This procedure will determine m more directly. Step 1 Adjust the external resistor 1 until the current through the galvanometer is 4 ma. m 1 1 m 1 G 2 m 2 2 A m 2 m 2 1 PHYS 0219 DC Circuits m 2 16 1 Step 2 Add a second external resistor 2 in parallel with the galvanometer and adjust it until the current through the galvanometer is 2 ma. B m
Assume that 10, 1000 and that 5.0. 2 m 1 A 5 1240 10 1 m 5 1250 4.00 ma B A B 5 5 1 1 2 m 1240 5 1245 m m 1 m m 4.02 ma This tells us that when we add 2 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 2 such that the current through the galvanometer is cut in half then: 2 m PHYS 0219 DC Circuits 17
esistor Capacitor (C) Circuits A capacitor is a set of two conductors separated by a small distance. Usually a capacitor is constructed from a set of parallel plates or a set of concentric cylinders. The symbol used for capacitors in schematics is as set of parallel plates: O The volume between the conductors can be vacuum, air or a dielectric material. Dielectric materials become polarized by the electric field across a capacitor and thus increase its capacitance. PHYS 0219 DC Circuits 18
When a capacitor is connected to a battery, positive and negative charges build up on the two opposite plates. This charging of the capacitor is nearly instantaneous. - + - + - A negative current flowing away from the negative terminal of the battery is just like a positive current flowing towards it. The total amount of charge that builds up is proportional to the voltage across the capacitor. q This can be turned into an equation by multiplying one side by a constant of proportionality called the capacitance C. q C PHYS 0219 DC Circuits 19
C C = Capacitance q Coulomb Farad (F) olt 3 mf 10 F 6 F 10 F 9 nf 10 F 12 pf 10 F The charging of a capacitor may be slowed down by placing a resistor in series with it the capacitor. + - 0 C The voltage change across the resistor and capacitor must equal the voltage of the battery, so: 0 C We can rewrite this using Ohm s law and the equation for the capacitance: 0 C This is actually a differential equation since: dq PHYS 0219 DC Circuits 20 q q 0 dt C Divide both sides by : 0 dq q dt C dq dt
0 dq q dt C q C e The solution for this differential equation is: 1 t C 0 Divide both sides by C and this becomes: 1 t C 0 e Charging Capacitor C is called the time constant. C olt Coulomb Coulomb second olt second 0 oltage () versus time (t) plot for a charging capacitor t PHYS 0219 DC Circuits 21
What happens if the capacitor is charged and the battery is removed? C The voltage change across the resistor and capacitor must now sum to zero volts: 0 C init As before, we can rewrite this using Ohm s law and the equation for the capacitance: 0 q dq q C dt C Divide both sides by : 0 The solution for this differential equation is: q dq dt init q C C e t C The initial voltage on the charged capacitor. Divide both sides by C and this becomes: e init t C Discharging Capacitor PHYS 0219 DC Circuits 22
init e init t C 1 ln ln init C oltage () versus time (t) plot for a discharging capacitor Take the natural log of both sides: t Plot ln versus time (t) 1 slope C intercept ln init t PHYS 0219 DC Circuits 23
Basic Procedure for C Circuits 1. Observe the charge and discharge curves for a capacitor. 2. Measure the voltage as a function of time for a discharging capacitor. 3. Make a plot of ln versus time and use the slope to determine the C time constant. 1 ln ln init C t 4. Measure the voltage as a function of time for the charging capacitor and use several data points to confirm the equation for a charging capacitor. 1 t C 0 e PHYS 0219 DC Circuits 24
NOTE: There are short answer analysis questions in the Participation section the informal lab report. emember to include these answers in your lab notebook as they will be part of your participation grade. PHYS 0219 DC Circuits 25