Introduction
The three main goals of the Experiment are to understand circuit elements, wire up simple circuits from circuit diagrams, understand currents and voltages in simple circuits, and their measurements in DMMs as well as apply Kirchhoff’s loop and junction rules to test circuit elements combinations. In Investigation 1, the group used Digital Multimeters as well as wires and cables to connect batteries in both series and parallel to observe the Effective Voltage. Then the group compares it to the theoretical voltages expected for each circuit. Then in Investigation 2, one finds the actual resistance of the 100 ohm resistor on the circuit element box as well as the Electromotive force of one of the batteries. Then one sets up a circuit with the batter, resistor, and several digital Multimeters. From there, one measures voltage and current to find the internal resistance of the battery. In Investigation 3, one measures voltages and currents for combinations of two resistors. The battery is replaced with a DC power supply such that it acts like it does not have any internal resistance One measures the actual resistance of the 470 ohm and 1000 ohm resistors. One also measures the power supply voltage and then connects it with the resistors in series to the Power Supply. Then one adds a Digital Multimeter to measure the current in the circuit. Then, one compares the total resistance of the two resistors with a calculated resistance. One also determines if the burden voltage affects measurements. One repeats this process for a parallel circuit to see how resistance, power, and current is different.
Investigation 1
Setup/Procedure
Since the Procedure is mainly to Setup the Experiment, the two are combined into one section for the purposes of each Investigation. The following equipment is needed for the Investigation:
· Two Flashlight Batteries in battery holders
· One DC Power Supply
· Two Digital Multimeters
· Circuit Element Box
· 8 Patch Cables with banana connectors
· 4 Alligator clips
Figure 1 shows the series setup of the two Batteries. V represents the Voltmeter from the Digital Multimeter while the other two objects are batteries. Figure 2 shows a similar setup except the batteries are in parallel with one another. The small balls represent the positive ends of the battery and the back represents the negative ends of the batteries.
Figure 1 Batteries in Series
Figure 2 Batteries in Parallel
The Digital Multimeter should be set as a voltmeter across the battery by using a patch cable to connect the positive terminal to the DMM’s positive voltage input and a second patch cable to connect the negative battery terminal to the DMM’s negative COMM input. Then one connects the voltmeter clips to one battery to measure the emf of one battery and then repeat this for the other battery. The one connects the two batteries together in series as shown in Figure 1 and measures the voltage. The positive end of one battery is connected to the negative end of the other battery and then each end is connected back to the voltmeter. The voltage is then collected. Then, one connects the two batteries in parallel as shown in Figure 2. The two positive terminals are connected together and same with the two negative terminals.
Results/Analysis
Table 1 below shows the collected values from Investigation 1. Voltage 1 and Voltage 2 are the voltages of each battery that were present in the circuits.
Table 1 Investigation 1 values
In theory, the Voltage of the series circuit should be the sum of the voltage of the measured Batteries. Equation 1 is used to calculate the theoretical series voltage for Investigation 1: Voltage=V_1+V_2=1.499 V+1.500 V=2.999 V (Eq 1.). One can find the percent error using Equation 2 to see if the measured meter value is consistent within 1%. The calculation is shown: Percent Error=(Theory-Experimental)/Theory*100=(2.999 V-2.995 V)/(2.999 V)*100=0.13% Error (Eq. 2). Since the percent error is below 1%, the measurements of voltage in series are consistent with the theoretical value. For the parallel circuit, the Voltage value should be the same as the voltage of one of the batteries. This means that since the batteries are both about 1.500 V, the parallel voltage should be 1.500 V. One can again use a percent error calculation to determine if the value is consistent:Perecent Error=(Theory-Experimental)/Theory*100=(1.500 V-1.490 V)/(1.500 V)=0.67% Error (Eq. 2). Since the percent error is below 1%, the measurement of the voltage in parallel is consistent with the theoretical value. Practical uses of batteries in series would be plugging in batteries for a flashlight because the voltage for the power output is the total voltage of both batteries. If the flashlight had the batteries in parallel, then the voltage output for the light would be lower and the light would have a lower intensity. Practical use of batteries in parallel would be wiring that usually occurs in a kitchen because a constant large output of voltage is needed for appliances that use a lot of electricity like refrigerators, dish washers, and ovens. If the batteries were in series, the voltage would be split between appliances and overall the efficiency of the circuit would be low. Potential sources of error in this lab may have resulted from a lack of knowledge in circuitry, improper set up of the circuit, improper wiring, and wear-and-tear on the equipment.
Investigation 2
Setup/Procedure
The following equipment is needed for the Investigation:
· Two Flashlight Batteries in battery holders
· One DC Power Supply
· Two Digital Multimeters
· Circuit Element Box
· 8 Patch Cables with banana connectors
· 4 Alligator clips
Figure 3 shows the Circuit with the voltmeter, ammeter, resistor, and battery. The A represents the Ammeter, the battery is to the left, the R is the location of the 100 ohm Resistor which is in parallel to the Voltmeter.
Figure 3 Investigation 2 Circuit.
For this investigation, first one should disconnect and use the DMM as n ohmmeter to measure and record the actual value of the 100 ohm resistor in the circuit element box. From there, one measures the electromotive force of one of the two batteries. One takes the battery and resistor and builds a circuit to measure the current through the 100 ohm resistor connected in series with the battery using Figure 3 without the Voltmeter component. One of the DMMs must be set to ammeter mode such that the positive input is 500 mA MAX and the negative input is the black COMM. To make sure that the DMM measures the correct type of current, one presses Shift and then DC V to measure DC I. One should then measure the current. A second DMM acting as a voltmeter should be added to the circuit to measure the voltage across the resistor by putting the voltmeter in parallel to the resistor. This circuit is shown in Figure 3. One then can calculate the resistor value and compare it to the measured value. Without taking apart the rest of the circuit, one would then remove the voltmeter from the resistor and use it to measure the voltage across the ammeter. From there, the group calculates the internal resistance of the battery.
Results/Analysis
Table 2 below shows the data and calculated values for this lab.
Table 2 Investigation 2
The Resistance was measured to be 104.37 ohms. It is 4.37 ohms and 4.37% higher than the theoretical voltage. The error is therefore 4.37 ohms. Since the nominal tolerance is 10%, this is acceptable. From the current and resistor voltage, one can now calculate the Experimental resistance using Equation 3 as shown:
R=V/I=(1.37 V)/(0.0132 A)=103.79 ohms (Eq. 3).
Then one can find the percent error between the two values to see if the experimental value falls within the meter precision: (104.37 ohms-103.79 ohms)/(104.37 ohms)*100=0.56% Error (Eq. 2). Since the precision is less than 1%, the theoretical and experimental resistance are consistent. To determine the internal resistance of the battery, the group used Equation 4:
r=(emf-V_resistor-V_burden)/I=(1.499 V-1.37 V-0.016 V)/(0.0132 A)=8.56 ohms (Eq. 4)
The internal resistance of the battery was calculated to be 8.56 ohms. Potential sources of error in this lab may have resulted from a lack of knowledge in circuitry, improper set up of the circuit, improper wiring, and wear-and-tear on the equipment.
Investigation 3
Setup/Procedure
The following equipment is needed for the Investigation:
· Two Flashlight Batteries in battery holders
· One DC Power Supply
· Two Digital Multimeters
· Circuit Element Box
· 8 Patch Cables with banana connectors
· 4 Alligator clips
For this experiment, one first measure the actual resistances of the 470 ohm and 1000 ohm resistors. R1 refers to the 1000 ohm resistor an R2 refers to the 470 ohm resistor. Then with the power supply off, one connects the DMM to measure the power supply voltage making sure it is in the DC voltage position. Then Power Supply is turned on and the supply voltage is measured. Then one connects the two resistors in series to the PS. One uses a DMM to measure the current in the circuit. After turning the Power Supply on, one measures and records the voltage across each circuit element. This is done by moving the position of the voltmeter across the circuit. Figure 4 shows the Voltmeter in different positions at which the voltage at each component is found. One then sums the voltage and compares it to the power supply. PS is the Power Supply, A is the Ammeter, and V is the Voltmeter.
Figure 4 Voltmeter Positions for Series Circuit.
One calculates the total resistance and compares it to that of the resistance of the ohmmeter. Then one, puts the resistors in parallel with the power supply and measures the voltage of the ammeter and two resistors again. Once this is done, the voltmeter is adjusted to an ammeter to measure the current along each resistor. Figure 5 shows the PS as the power supply, A as ammeter, V as the voltmeter, and V/A as voltmeter and ammeter to measure the voltage and current along each Resistor
Figure 5 Volt and Ammeter Positions for Resistors in Parallel.
Results/Analysis
Table 3 shows the Data and partial calculations for Investigation 3.
The actual resistance of the 470 ohm and 1000 ohm resistors are 479.07 ohms and 1018.6 ohms respectively. This means that the error for each resistor is 9.07 ohms and 18.6 ohms respectively using Equation 5:
Resistance Error=Actual-Theoeretical=479.07 ohms-470 ohms=9.07 ohms (Eq. 5)
Resistance Error=Actual-Theoeretical=1018.6 ohms-1000 ohms=18.6 ohms (Eq. 5)
To find the tolerable error in resistance, one would use Equation 6 as shown below:
Resistance error= √((9.07 ohms)^2+(18.6 ohms)^2 )=20.69 ohms (Eq. 6)
First, the group worked with calculations for the series circuit. The sum of the voltage drops is shown in Equation 7.
V_total=V_(1000 ohm)+ V_(470 ohm)+ V_Ammeter=3.165 V+1.5 V+0.27 V=4.935 V (Eq 7.)
Using Equation 2, one can find the percent error between the Power Supply Voltage and the Experimental Voltage (5.009 V-4.935 V)/(5.009 V)*100=1.5% error (Eq. 2). This percent error is greater than then 1% allowed which could mean that not accounted for the burden voltage may have caused an error in the measurements. This would mean the burden voltage is about 0.074 volts. To find the power dissipated across each resistor, one would use Equation 8.
Power=V^2/R=(1.5 V)^2/(479.07 ohms)=0.004697 Watts (Eq. 8)
Power=V^2/R=(3.165 V)^2/(1018.6 ohms)=0.009834 Watts (Eq. 8)
One can then find both the experimental and the theoretical resistance using Equation 9 and Equation 10 respectively.
R=V_total/I=(4.935 V)/(0.00313 A)=1577 ohms (Eq. 9)
R=R_1+R_2=479.07 ohms+1018.6 ohms=1498 ohms (Eq. 10)
One can now also find the difference in Resistance between these two values. Using basic arithmetic, one finds that the difference is 79 ohms which exceeds the permissible 20.69 ohms. This means that the measurements do not agree for the rule for addition of two resistors in series. This also suggests that it could be due to the unaccounted burden voltage. Potential sources of error in this lab may have resulted from a lack of knowledge in circuitry, improper set up of the circuit, improper wiring, and wear-and-tear on the equipment. Then, the group started to focus on the parallel circuit. The group again used Equation 9 to find the experimental Resistance and then Equation 11 to find the theoretical Resistance.
R=V_total/I=(4.995 V)/(0.0163 A) (Eq. 9)
1/R=1/R_1 +1/R_2 ,R=326 ohms (Eq. 11)
The difference in the number of ohms is 20 which is within the permissible range of 20.69 ohms. So the measurements agree with the rule for addition of two resistors in parallel. Equation 12 is then used to sum the experimental current values and then Equation 2 is used again to compare the experimental value to the first measured current value.
I=I_1+I_2=0.0108 A+0.0052 A=0.016 A (Eq. 12)
(0.0163 A-0.016 A)/(0.0163 A)*100=1.84% (Eq. 2)
While these values are close, they do not fall in the 1% permissible range which could again suggest an unaccounted burden voltage perhaps. One did not also account for the current across the voltmeter which could be a source of error. Equation 8 was used once again to calculate the dissipated Power from each resistor.
Power=V^2/R=(4.995 V)^2/(1018.6 ohms)=0.0245 Watts (Eq. 8)
Power=V^2/R=(4.995 V)^2/(479.07 ohms)=0.0521 Watts (Eq. 8)
Clearly, the power values for the Parallel circuit (0.0245 Watts and 0.0521 Watts) are greater than the Power values of the Series Circuit (0.009834 Watts and 0.004697 Watts). This is because the Voltage is split for a series circuit which would decrease the value of the power while the voltage is conserved for the resistors in parallel. Potential sources of error in this lab may have resulted from a lack of knowledge in circuitry, improper set up of the circuit, improper wiring, and wear-and-tear on the equipment.
Conclusion
The main goals of this lab were fulfilled. The group was able to study and understand circuit elements as well as figure out how to wire circuits based on provided circuit diagrams. This involved using resistors and batteries in parallel. The group learned from Investigation 1 that total voltage is conserved for batteries in parallel to equal that of one battery, but in series it is cumulative. In Investigation 2, the group understood the impact of burden voltage as well as the internal resistance of a battery on the total voltage experienced by a resistor as it differs from the voltage of a battery. The group also understands that internal resistance exists within each battery. Also, wear-and-tear impacts the resistance of a 100 ohm within the circuit box. Investigation 3 showed to the group that power dissipated by resistors in parallel is greater than the power dissipated by resistors in series. Also, resistance can differ greatly between theoretical and experimental values for parallel and series circuits. Split values like voltage for resistors in series and current for resistors in parallel might not necessarily account for all of the current which can be lost due to some sort of internal resistance or the Ammeter/Voltmeter itself. This lab was successful in teaching students the fundamentals of circuits. Future applications of this lab may be present in designing circuits as an electrical engineer.
