16April2014

Testing the Loop Rule with Real Circuits

The circuit board was set up to determine the different currents in circuit. Our group choose not to use the potentiometer in our circuit board because of the large source of error it created, instead to be more efficient we choose to use 2 1kOhm resistors to gather our data. We will find the percent discrepancy using the loop rule to determine the theoretical calculation of the different currents and compare it with the actual value found in the circuit board above.  

 The current that is found running across the 3.6k Ohm resistor was found to be 0.148 A.

The current that is found running across the 2k Ohm resistor was found to be 1.005 A. 

The current that is found running across the 2.2k Ohm resistor was found to be 1.151 A.

In this picture you can see the schematic for the circuit we set up. In class we used the loop rule to find three equation with three unknowns. We used a calculator to determine the different currents that run across each resistor which gave us our theoretical current values at each resistor. We found a percent discrepancy for the current over the 2.2kOhm resistor to be 0.96%, 2kOhm resistor to be 0.60%, and 3.6kOhms resistor to the  5.7%. The precent discrepancy tell us that loop rule is a effective method of determine the current that runs across the resistor. 

Resistors in Series and in Parallel 

The resistance on the resistors was determined in two different configurations series and parallel with the volt meter in order to determine a relationship with the different configurations. 

We found that when the resistors are in series they are additive. We observed when the resistors are in parallel they are additive: 1/(Rtotal)=1/R1+1/R2+...1/Rn where n is the number of resistors in parallel. 

In this picture we used the relationship of the configuration of the resistors to determine the total resistance of the circuit when these configuration are combined above. The theoretical resistance was determined to be 52.5ohms

Here we can see the configuration of the resistors like the diagram above and the expected resistance measured with the voltmeter was determined to be 50.0 ohms. 

The percent discrepancy was determined to be 4.76% which is within the 5% error expected of the ceramic resistor as seen in the picture above.