Series and Parallel Circuit Lab Report

7/25/2016

LAB REPORT 1 Series and Parallel Circuits

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Introduction Parallel and series circuits are able to be reduced to a single, equivalent resistance. This experiment was to determine the actual resistance of 4 series and parallel circuits by using the voltage and current across the circuits and comparing this value with the theoretical calculations of the circuit resistance.

Theory A resistor is typically a device that obeys Ohm’s Law and has a resistance of value R, measured in Ohms (Ω). The equivalent resistance for a series circuit can be found using the total sum of the resistors (Equation 1). R= R1+R2…+Rn

(Equation 1)

The equivalent resistance for a parallel circuit can be found using the reciprocal sum of the resistors (Equation 2). 1/R= 1/R1+1/R2…+1/Rn

(Equation 2)

Ohm’s Law is the product of the current (I) and the resistance and is equivalent to the voltage of the system (Equation 3). V = IR (Equation 3)

Experiment The theoretical resistances were found using the values of the resistors and using equation 1 and equation 2. The values for the theoretical resistances can be found in table 1 on page 3. In order to determine the actual resistance of the resistors in each circuit a constant DC voltage of 15 was applied to each circuit. The computer was used to find the current across the circuit and the precise measurement for the voltage (14.97 V). These values were used in conjunction with Ohm’s Law in equation 3 in order to calculate the actual resistance by dividing the voltage by the measured current.

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Data

Figure 1 Circuit Diagram 1: Series Circuit

Figure 2 Circuit Diagram 2: Parallel Circuit

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Figure 3 Circuit Diagram 3 Simple Series Parallel Circuit

Figure 4 Circuit Diagram 4 Complex Series Parallel Circuit

Table 1 Theoretical Resistances

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Table 2 Measured Resistances with Percent Differences

Table 3 Tolerance of Theoretical Resistance in Ohms

Analysis Theoretical vs Measured Resistance

Theoretical Resistance (Ω)

Measure Resistance (Ω)

Figure 5 Theoretical vs Measured Resistance

Discussion In figure 5 on page 4 the measured resistance of each circuit can be seen as lower than theoretical resistance. Table 2 on page 3 displays the measured current of each circuit with the calculated resistance. The calculated resistance for circuit diagram 1 is 759.9 Ω. In comparison to the theoretical resistance for this circuit, 890 Ω, there is a 15.77% difference. This is far above the tolerance of -5%, which would be 845.5 Ω. Circuit 2 has a calculated resistance of 194.7 Ω and a percent difference of 6.41%. The -5% tolerance of the theoretical value for this resistance is 197 Ω. This is the circuit with the

5 lowest percent difference. Circuit 3’s calculated resistance is 282.5 Ω with a percent difference of 8.51%. The -5% difference for the theoretical value for this circuit is 292 Ω. Circuit 4 has a calculated resistance of 349.8 Ω in comparison with its theoretical resistance of 383.3 Ω the percent difference is 9.14%. This is a higher percent difference than the -5% tolerance of 364.1 Ω.

Conclusion The differences in the calculated and theoretical values for the circuits compared to the tolerances of the theoretical values can be attributed to some error in the system. If it can be assumed that the tolerances are correct for each resistor and they are not defective then the differences would stem from somewhere in the system to measure the current for each circuit. This would mean that there is a resistance in either the lines that connect to board to power the circuit or in the springs that connect each of the components. The differences could also stem from not calibrating the system before beginning the experiment.